Good morning, towards the end of the previous lecture, we saw the del or nabla operator operated on ordinary scalar and vector functions. Now, we will consider composite operations involving the del operator, always keep in mind that the operator del is a linear operator and therefore, whether applied as gradient divergence or as curl, they distribute over a sum of functions. Next, we consider the del operator applied over products of field functions. Four cases may arise, the product of two scalar fields is again a scalar field, the product of a scalar field and a vector field is a vector field and the product of two vector fields can be in two ways, one is the dot product which is a scalar and the other is a cross product which is a vector. When we apply the del operator on these four composite functions, these are the way to apply the operator. So, the gradient of phi into psi turns out to be this, the divergence of phi into v turns out to be gradient of phi dot v plus phi into divergence of v, the cross product the curl of phi v turns out to be gradient of phi cross v plus phi into curl of v and so on. So, these representations, these expressions you can work out, if you open, if you expand these expressions term by term and then simplify. When we go further and operate the gradient divergence and curl of a scalar or a vector function by the del operator once more, then we get what we call as the second order differential operators. Now, grad phi is a vector quantity, it is a vector function. So, you can apply del in two different ways through the dot product or cross product and accordingly, you get divergence of grad phi and curl of grad phi. When you consider the curl of v and consider applying the del operator over that curl of v, then again you can apply it in two ways, one is through dot product and the cross product. Therefore, you get two further second order operators, one is div curl and the other is curl curl.  So, that gives you these five second order differential operators and two of them give us very important information, that is curl grad phi is identically 0 whatever may be phi. Similarly, div curl v turn out to be identically 0 whatever is the vector function v. So, what these two mean is that curl of a gradient is always 0 and divergence of a curl is always 0, then divergence of the gradient function grad phi turns out to be the Laplacian del 2 phi. So, curl curl and grad div these two have this relationship between them. So, these give you some of the relationships that the second order differential operators always the first is the line integral along a curve. So, if you have a vector function v, then along a curve if you take its integral that means take its integral that means that you have this curve and from this point to this point if you want to take the line integral of a vector function that means you take v dot a small length element a small vector element displacement element in along this curve. So, v dot dr such v dot dr components if you keep on adding from the starting point to the end point then you get the line integral integral along a curve of this particular vector function along curve t.  So, if the curve is parameterized in this manner over an interval a to b for t then this line integral reduces to an ordinary definite integral from t equal to a to b like this. So, v d dot dr becomes v dot dr by dt into d t. So, v dot dr by dt turns out to be a function of t which you can integrate from t equal to a to b. These are some important statements which mean the same situation. So, all of these are equivalent statements for simple non intersecting curves or paths contained in a simply connected region these all of these are equivalent statements v x d x plus v y d y plus v z d z this quantity here this differential quantity here is an exact differential that will mean the same thing as the that the vector function v is the gradient of some scalar function some scalar field phi and that also means that if this is a perfect differential that means it can be integrated and the integral of this will be something which does not depend on the path along which the integral has been performed. So, for that kind of a function v which is the gradient of some scalar function whether you integrate from this point to this point through this curve or along this curve or along this curve the result will be same. And this also means that if the curve c is a closed curve then the point from where you start the it is the same point where you end and that means the integral line integral along a closed curve circulation represented with this circle on the integral sign that turns out to be 0 around any closed path. It also means that curve v is equal to 0 that is clear because v itself is the gradient of some scalar field. So, it is curve must be 0 this in that in terms of relevant physics means that the corresponding field v is a conservative field. The second integral that we define is a surface integral this is defined over a surface element. Now, d s is a differential surface element and its magnitude is the area of that small surface element and the direction is along the normal to that surface element. So, if you effect this dot product and then integrate that all over a surface patch then you get the surface integral of the vector field v over that surface patch s. And for this the surface patch s must be orientable that is it should be clear which side of the surface we are talking about that is only those surfaces for which one side of the surface and the other side of the surface are clearly identifiable. Now, if there is a parameterization of the surface in terms of two parameters u and w then this small surface area area element d s can be found from this and we can work out the normal also unit normal which is r u cross r w divided by this magnitude. And therefore, when we insert the relationship between in this expression then v dot n d s in place of n we get this cross product divided by its magnitude.  So, that magnitude gets cancelled and finally, we get this as the integrand and we can integrate over the region r in the u w plane the parametric plane. Finally, we have got the volume integral which operates over a differential volume. So, volume integral you can evaluate for scalar field functions as well as vector field functions. So, in terms of these integrals we have quite a few important theorems which are called the integral theorem. The first among them is the Green's theorem in the plane. Consider r as a closed bounded region in the x y plane like this region is r bounded by a closed curve c c is the boundary of r this curve a c b d is the curve c.  Then Green's theorem in the plane states that the line integral of the vector function f having f 1 and f 2 as component turns out to be the same as the double integral of this quantity on the entire region r. Now, this gives you a relationship between the double integral over a region and a line integral over along its boundary. Now, among the three theorems that we are going to discuss the line of proof for the first of these the Green's theorem in the plane we will discuss in detail to give you the clever of the proofs of these theorems and for the rest of them we will summarize the theme of the proof only. So, the way you try to prove the way we tend to prove Green's theorem in the plane is first by considering a simple domain in which any line parallel to the coordinate axis parallel to y axis or parallel to x axis cuts the boundary of the region or cuts the curve c only at x axis.  So, because we consider such a simple region first so that will mean that the entire curve c can be split into two parts one a c b and the other a d b first one can be called the lower half and the second one can be called upper half because any line parallel to y axis cuts it only at two points one is a lower point the other is the upper point. Similarly, since a line parallel to x axis like this also cuts it at at most two points. So, in another way we can subdivide the boundary into two parts one is c b d the right half and the other is c a d left half. Now, if we can do that then consider the one of the double integrals from here say del f 1 by del y d x d y. So, first we consider that and del f 1 by del y d x d y this double integral over the region. So, what we can say is that first we will integrate it with with respect to y and then x. So, we interchange the order of these differentials d y d x and as we do that first integral is with respect to y and y varies from the lower part to the upper part. So, let us represent this lower part as a function y of x call it y 1 of x the lower part of this boundary is a curve that can be represented as y 1 of x the upper part as y 2 of x. So, that means for the first integral with respect to y the lower limit is y 1 of x the upper limit is y 2 of x. So, that is this y 1 x to y 2 x and this integral will be next integrated with respect to x from x equal to a to x equal to b. That means all these vertical strips will be then added together from this end to that end. If we do that then del f 1 by del y integrated with respect to y. So, that will simply give us f 1 f 1 at the upper limit minus f 1 at the lower limit. So, f 1 at the upper limit is f 1 of x and y 2 and f 1 at the lower limit is f 1 of x and y 1. Now, note this that this has to be this has to be integrated with respect to x from a to b over along y 2 the first one. So, first one along y 2 has to be integrated from a to b. We can say that we will integrate its negative from b to a that means x equal to b to x equal to a. If we do that then this gets changed to negative of this with the corresponding swapping of the limits of the integral. Now, see f 1 of x y 2 and here f 1 of x y 1 both signs negative. So, you find that b to a is this integral and a to b is this integral this is along y 2 this is along y 1. So, what this is going to mean from a to b along y 1 and then from b to a along y 2.  So, you have got a closed line integral over the entire boundary. So, that means that the these two terms together will mean minus common minus sign the line integral of f 1 over the entire curve c that shows that del f 1 by del y double integral over r turns out to be minus the cyclic integral or circulation of f 1 f 1 d x. So, the second term here turns out to be equal to the first term here. Similarly, by dividing this curve into two parts the left half and the right half as x 1 y from here to here and x 2 y from here to here. You can establish the equality of this part with this part that is the first double integral from here as the same as the first line integral from this side the second line integral from this side. So, as you do that in this manner first integrated with a set to x from this limit to that limit and continue to get the next integral with a set to y and then you add them together then you find them that this turns out to be the same as this and as you take the difference of the two you get the final result which is this. Now, if you carefully evaluate if you carefully check this you will also find that this turns out in alternative form the this one is the line integral f dot d r f is f 1 i plus f 2 j in the plane there is no k component. So, then this is f dot d r and on this side you find that this turns out to be the magnitude of the curl f and its direction is k because i and j are both in the x y plane. So, curl will turn out to be in the direction k and if d x d y is an area element in the x y plane then its direction as a as area is a vector quantity the corresponding direction will be again in the k direction. So, the magnitude will remain and k cross k dot k will turn out to be unity.  So, in alternative form this same relationship the result of the Green's theorem in the plane means that the line integral of a vector function turns out to be along a closed curve c turns out to be same as the surface integral of the curl of f over a surface element bounded by this same closed curve c. Later we will see that this in a more general form turns out to be the statement of Stokes theorem. So, that way Green's theorem in the plane is actually a special case of Stokes theorem which is more general. Now, recall that we consider this entire curve for a simple region. Simple region in the sense simple domain in the sense that any line parallel to one of the any of the coordinate axis cuts the curve c in at most two points. Now, if that is not the domain if the domain is like this not only general, but also multiply connected there is a hole also this part is not included in the domain. So, for that also we can have Green's theorem and the proof is not very complicated because for this kind of a domain we can always decompose this domain into simpler regions simpler domains in such a manner that each of the component domains satisfies this kind of a requirement. And then over every component over every component domain we can prove this and then we just sum up all these components 1, 2, 3, 4, 5, 6, 7 components we sum up together. The double integrals are directly additive they add up totally and we get the complete double integral by the simple sum. For the line integrals here what we find is that as we add them up then the actual boundary of the original domain both the outer boundary and the inner boundary is covered only once. On the other hand the spurious boundaries which was due to our subdivision of the domain gets actually circulated twice as a part of this sub domain it got circulated once from lower end to upper end as a part of this region it got circulated once it got included once from upper point to the lower point. That means this inner boundary this spurious boundary between two sub domains which was not part of the original boundary gets included in the line integral twice once along this way and the next time along this way. And in the algebraic sum they get cancelled for each of the inner boundaries the spurious boundaries that is the same thing that is going to happen. So, in the final sum the line integral that remains caters to the actual original boundary of the given domain and removes all the contributions from the spurious boundaries because they are traversed twice in opposite senses. So, they cancel each other. So, this way Green's theorem in the plane can be applied to this kind of domains also. Now, the next important theorem is the Gauss theorem which has a lot of application lot of fundamental interpretation in physics. So, for that we have a closed boundary region represented as t and its boundary s which is a piecewise smooth closed orientable surface. And over the entire region we have got defined a vector function f which is first order continuous that means it is continuous and its first order derivatives are also continuous. So, for that kind of a function the Gauss theorem or the divergence theorem says that the volume integral of the divergence of the vector function f over the entire volume is the same as the surface integral of the function itself of the vector function itself over the boundary of the region that is the surface integral is evaluated over the boundary s. Now, this is actually a direct result of the interpretation of the definition of divergence to the finite domains that is whatever is the meaning or interpretation of the quantity divergence for an infinitesimal domain around a point the same theme when extended to finite domains the corresponding extension turns out to be this divergence theorem. So, when you open these expressions then you get this divergence of f is this the volume integral of that is this over t and f dot n gives you this scalar quantity and you get the surface integral of that with scalar surface area element d s. So, this equality is the result of Gauss divergence theorem. If you want to establish this result what you try to do is that you try to establish the equality of this term by term that is the third triple integral from here is going to be equal to the third double integral from here the z component to z component and so on. So, term by term equality you can establish that is del f by del z triple integral will be equal to the surface integral of this part and so on for all three parts. So, for this also first we consider a region a volumetric region such that the boundary of which is cut by any line parallel to x axis y axis z axis at most in at most two points not more than that first we consider that kind of a region over that we establish the equality and then for extension to general regions we again subdivide the general region into many such simpler regions which satisfy this requirement and sum up the contributions. And in the case of Green's theorem in the plane the direct additive sum was on the double integral here the same thing happens for the volumetric and there the boundaries were segments of lines or curves which were traverse the inner courier boundaries were traverse twice in opposite senses here the boundaries will be surface elements and they whatever courier surface element is going to be used from one side in one of the double integral one of the surface integral for one region one sub region it is going to be considered in the other sub region as from the other side. And that is why those courier surface elements in the final sum get cancelled out and you get the actual surface integral over that surface which is the part of the original domain. Now, we will omit the detailed proof of this step by step and you can follow the proof at leisure later and work out the proof in the same lines. There are two further important identities or results called Green's identities which also work with a region volumetric region T with its closed surface boundary S as required in the premises of Gauss theorem. And when we apply Gauss theorem over certain functions in certain manner that is once on phi grad psi and then on psi grad phi then as a direct consequences of Gauss theorem we can establish these relations which have a lot of important applications in many fields. The third important theorem of vector calculus is the Stokes theorem that is that makes reference to not a closed surface, but an open surface so in this manner. So, suppose this is an open surface S and this is the boundary of the open surface. Now, note that with the same boundary of the open surface with the same boundary, boundary being a closed curve you can have many different surfaces. For example, if you have a ring and then here is a net. So, if you have with which you try to catch something. So, now you can go on changing the shape of this net, but the ring which is the boundary of the net remains the same. So, all these surfaces all these surfaces will have the same boundary and these are all open surfaces. This side it is open. So, that is why you get this boundary. Note that a closed surface will have no boundary. For an open surface there is a boundary. So, even the planar region if the if this curve is a plane curve then the planar region bounded by this curve is also one such surface and that kind of a surface we encountered in the case of Green's theorem in the plane. So, this is a surface S, one of these is taken as S and the boundary of the open surface S is this curve this closed curve C. Now, if the if there is a field function first order continuous field vector function f defined over this entire region.  That is the statement of Green's theorem Stokes theorem in which the unit normal that you need to use here is given by the right hand class rule on C. That is since it is an open surface. So, whether to take the normal in this way or in this way has to be decided both are valid, but it will depend on which way we are traversing C. So, as we are traversing C. So, if we put our right hand along the arrow like this, then whichever way the thumb will point out that works out to be the n not this. So, if we point to the arrow by the clasping of the right hand in whichever way the thumb points through the surface that is the direction of n to be used here in this context. Now, we will again omit the proof of this and as a special case the Green's theorem in the plane the proof of that we have already seen. So, here you will find that if we consider the surface region S to be a region in the x y plane itself, then you will find that we will recover the Green's theorem in the plane as we have studied earlier. We will bypass the proof of this. So, the important points to be noted from this lecture or this lesson are the del operator that the del operator applied in three different ways on scalar and vector functions on scalar function you get radiant on vector functions through dot and cross product you get divergence and curl. The way we have the composite and second order operators on field functions, then next the line surface and volume integral and the three important theorems which are Green's Gauss and Stokes theorems and these theorems are important in the physics and engineering of large number of systems through their applications. So, in the exercises of this chapter in the book, you will find several important problems from physics as well as from applied mathematics where some of these theorems are applied directly to break the problem or reduce the problem into much simpler situations. In these two lectures on vector calculus by avoiding some of the long proof we have saved some time. So, let us take some examples on vector calculus. Some examples on physics and engineering problem as well as on applied mathematics problem pertaining to the scalar and vector field are given in the exercises in the text book in chapter 18. I strongly advise you to attempt those exercises particularly the exercise on Maxwell's equation because that takes you through a complete exposure to almost all the important issues discussed in this lesson. Now, we consider one problem on parametric curve. This is actually the problem of 17-6 of the text book that we are following. In the appendix of the book corresponding to this problem three approaches have been outlined. Here I will elaborate one of the approaches. The problem is to verify or check whether these two parametric equations represent the same curve or not. This is the first curve and this is the second curve. Now, you will note very easily that the first curve is evidently a circle with origin at the center and radius free lying in the x y plane that much is very clear. Now, we need to check whether R 2 of t also represents the same curve. So, for that we try to transform R 2 in such a manner that it gets connected get started from the same point where the first curve starts. So, for R 1 for the first curve let us see what is R 1 at t equal to 0 the starting point. So, if you put t equal to 0 here it is an i. If we put t equal to 0 here then we get R 1 0 as 3 i its derivative R 1 t the derivative of the first curve the tangent vector that you will get as 3 sin t i plus 3 sin t i plus cos t j at t equal to 0. If we evaluate this tangent vector then we get this is 0 and from here we get 3 j that means that the curve starts here at 3 0 3 0 0 actually in the 3 d 3 0 0. So, in x y plane this curve is in planar curve in x y plane. So, we are making the diagram only in the x y plane. So, it starts from 3 0 and since it is a circle it must start like this and that is why the tangent vector is found to be in the direction j. So, this is the way the circle proceeds. So, this is the point of our interest right now. Now, if this is the tangent vector then what is the unit tangent. So, unit tangent at the starting point for the first curve is j at the starting point note that you can write u 1 of 0, but to make the notation simple currently we are writing here understood is the fact that it is the starting point which is being analyzed right now. Similarly, we can find out the second derivative of r 1 t and then we put the value t equal to 0 in that second derivative which will give us this as minus 3 i which will mean that the unit principle normal is minus i for the first curve. So, if unit tangent is there unit principle normal is there then from these two we can work out what is the binormal u 1 cross p 1. So, j cross minus i we will get that as k. Now, this much we have in hand now we will try to find out the same quantities from r 2 and then try to work out the transformation which will bring u 2 to u 1 p 2 to p 1 and b 2 to b 1 and r 2 at pi by 4 to r 1 at 0. That means we want to match the starting point and we want to match the select frame at the starting point. So, we want to match the point r 1 and u p b point r u p b at the starting point of both the curve. So, we leave the first curve at its place and the second curve we try to bring here. So, for that purpose please make note of this and we have let me mark here unit tangent is here unit principle normal is here and of course, b 1 is perpendicular out of the board because of the cross product. So, now we get rid of this because all the information from here is actually available here as well this is the starting point. Now, the same things we try to evaluate from here. So, for the starting point we put t equal to pi by 4. So, as we put t equal to pi by 4 here. So, pi by 4 into 2 that is pi by 2. So, sin pi by 2 is 1 cos pi by 2 is 0.  So, this is the starting point for the second curve as it is given. Now, if we develop the first derivative and second derivative that also you can similarly do finding derivative is not very complicated. So, I am omitting that and giving you the result if you evaluate the first derivative of this that is r 2 prime t and then at t equal to pi by 4 you evaluate that then you find that you get this as minus 4 i plus 2 j plus 4 k. You must evaluate this expression for the derivative and then verify that this indeed is what you get. Similarly, differentiating that again for the second derivative and inserting the value pi by 4 in place of t you would find minus 8 i minus 8 j minus 4 k. So, from here you can work out the unit tangent and unit principle normal between these two. So, from here you will get u 2 at the value pi by 4 at the value t equal to pi by 4 that is at the starting point as now this is minus 4 to 4. So, what will be the magnitude? Magnitude will be 6. So, you divide by 6. So, you get minus 2 by 3 i plus 1 by 3 j and plus 2 by 3 k this turns out to be the unit tangent at the starting point for the second curve. Now, this in the first case as you saw it was very clear that the tangent vector came to be in the direction j and the second derivative appeared in the direction minus i which are orthogonal to each other perpendicular to each other anyway. So, we did not have to subtract the component of r double prime from the direction of u. If the same thing happens here also then it is fine otherwise we will have to subtract that. So, whether this r prime and r double prime are perpendicular to each other that you can check otherwise we would have to subtract. So, you get 32 minus 16 minus 16. So, the dot product between these two is 0 that means this is indeed perpendicular to this. So, that makes our life easy. So, the unit vector along this direction itself is the unit principle normal. So, you get the unit vector in this direction and divide by 12. Yes, the magnitude of this is 12. So, you divide by 12 and you get minus 2 by 3 i minus 2 by 3 j and minus 1 by 3 k. So, this you get as the principle unit principle normal and from these two you can work out b 2 as the cross product which turns out to be 1 by 3 i minus 2 by 3 j plus 2 by 3. Now, we have the starting point of the curve r 1 here and its u p b serif and net frame oriented in this manner. And for the second curve also we have got the corresponding pieces of information r 2 at the starting point and u 2 p 2 b 2 at the starting point the point and the serif and net frame. Now, if the two if the two parametric equations these two represent the same curve then if through a rigid body motion a displacement and a rotation. If we can bring this r 2 and this u 2 p 2 b 2 in the location and orientation of the first curve r 1 then the complete curve should match. So, let us try to do that. So, we ask what rotation transforms these three vectors in the direction of these three vectors this is the question we ask. So, suppose that rotation matrix 3 by 3 rotation matrix is r.  But that is not very different because the two rotation matrices are transposed of each other. So, if we try to do this we are going to do it like this because the matrix that will appear here will be easier to invert. The matrix that would come from there will be more complicated to invert and we must invert one of the two matrices. So, r into u 1 what is the column representation of this vector u 1 u 1 is j that means 0 1 0 0 i plus 1 j plus 0 k. So, u 1 is 0 1 0 0 1 0 0 1 0. So, p is minus 1 0 0 that is minus i minus 1 0 0 and b is the z vector k that is 0 0 1. We find that we want the rotation matrix which transforms u 1 to u 2 p 1 to p 2 and b 1 to b 2. So, u 1 to u 2 r into first column of this should be here that is the vector u 2 there. Similarly, r into p 1 should be p 2 and finally, r into b 1 should be b 2 that is this. Now, we want to determine r. So, we need to post multiply the matrix on the right side with the inverse of this which is quite simple. So, let me give you the expression for that r which you can verify later. Now, it is actually quite simple what we need to do is to interchange these two columns on both sides. So, as we interchange these two columns we get 1 here and minus 1 here then the first column we should make negative because this is minus 1. So, that will immediately make this identity matrix and whatever is there will be the product of this with its inverse from the right side. So, this tells us that the matrix r is the negative of this column comes first this column goes next and the third column remains in its own place because this is 0 0 1. So, those column operations which will make it identity the corresponding column operations done here give the value of the rotation matrix r. Now, this is the matrix r which operated over u 1 p 1 b 1 takes it to u 2 p 2 b 2 and what we are looking for is actually the inverse transformation because we want the second curve to come and merge here if they turn out to be the same curve. So, we need the inverse of this rotation matrix and inverse of rotation matrix is just transpose. So, we transpose this matrix. So, these two exchange their places these two exchange their places in this case we do not have to make any change because they are same and these two exchange their places. So, this transformation applied on the second curve will bring it to the first curve if they turn out to be the same curve. So, that is the check that we have to perform. So, the second curve transformed through now first orientation only till now we have not given the position transformation. So, the orientation of the second curve is changed in order to match the orientation at the starting point. So, let us call it r 2 tilde that will be r transpose into what is r 2 given. So, that means that this matrix multiplied to the vector now this i j k the way it is written the first entry will be here the second entry the j entry will come here and the k entry will come here. If we multiply this matrix with this completely then we get r 2 t r 2 tilde t this one as 3 sin 2 t plus 10 by 3 minus 3 cos 2 t plus 8 by 3 3 this is after turning it. So, now the orientation of the second curve at the starting at its starting point is the same as the orientation of the first curve at its own starting point. That means now if they are the same curve then this curve and that curve now have taken parallel cross trails. Now to get the second curve here we need to apply a displacement. So, for displacement we will need the displacement that is needed say delta r will be this r 2 tilde at its starting point which is pi by 4 minus this r 1 at its own starting point and earlier we saw the starting point of this r 2 at pi by 4 and that was 3 i plus 4 j plus 5 k from that we subtract this which is 3 i. So, the rest of it we get 4 j plus 5 k r 2 has been transformed r 2 has been transformed so better we evaluate this. We evaluate r 2 tilde at pi by 4 from here fresh because during rotation its starting point has gone to some other locations. So, put pi by 4 here so that means sin pi by 2 is 1 so 3 plus 10 by 3 from which we subtract this 3 i so only 10 by 3 will remain and then minus 3 into cos pi which is 0. So, this 8 by 3 minus 0 8 by 3 remains and finally the k part which is 3 minus 0. So, we have got 3. So, this is the displacement which we have to give in a negative direction to r 2 tilde to bring it here. So, now let us call this now this r 2 tilde was the rotated version of r 2 now r 2 bar will be the translated further translated. So, this r 2 bar will be this r 2 tilde minus this delta r. So, what we will find from here if we subtract this then we will get 3 sin 2 t i minus 3 cos 2 t j and 0. So, now we find that this is also a circle in the x y plane starting from here no question about all this. But still you find that the equation of this and the equation of this do not exactly match because there is a change of the parameterization. If you now try to reparameterize this same curve with a little different parameter say with tau equal to 2 t minus pi by 2 then you will find that the equation of this transforms exactly to the equation of this in terms of tau. So, whatever is this equation in terms of t the same equation here you will get in terms of tau you will get 3 sin 3 cos tau 2 t minus pi by 2 you will get 3 cos tau i plus 3 sin tau j and that will also transform the starting point in the first curve the starting point was 0 in the second curve till this point the starting point is pi by 4. When you put that pi by 4 here you will find that the starting point of tau will be 0. So, that way you will find that through these changes rotation to make the set the difference of the two curves parallel then translation to make them merge at the initial point and then reparameterization will show that the two curves exactly have the same equation. So, up to this stage the curve has actually come here, but its parameterization is different. So, at different values of the parameter it is going to different points rather than tracing the same curve at the same parameter values. So, this reparameterization will convince that the two equations are found to be exactly same. So, far in the discussion on vector calculus and next lecture onwards we will start our next module on numerical analysis starting from polynomial equations. Thank you.


Hi, my name is Jitske and I'm going to tell you about my bachelor's program at Tilburg University, online culture, art media and society. Within online culture, you study cultural phenomena in an increasingly digital and globalised society. You delve into new ways of communicating, community building and policymaking. And you explore the role online and offline media and artistic expressions play in this. In the program, you explore the influence globalisation and digitalisation have on politics, identity and on how we shape and express our opinions. Think of questions such as how do politicians and artists use social media? What is the impact of living in a filter bubble when algorithms decide what information you see? And how does being in touch with people from all over the world affect our cultural identity? Apart from studying digital culture, you also actively contribute to it. By publishing papers and reviews on Digit Magazine. This online platform is unique to the program and attracts readers from all over the world. In your first year, you will become familiar with key insights and theories about digital culture and the role artists and intellectuals play in society. In your second year, you will specialise by choosing one of three tracks. The digital media track focuses on how digital media shaped today's societies. In the global communication track, you study how globalisation influences individuals, organisations and communities and how they interact. In the third track, Art in the Public Sphere, you study the role of art and popular culture in society and in shaping debates and opinions. In your third and final year, your minor allows you to further personalise your program. You can choose courses from other programmes at Tobog University, another university in the Netherlands or even abroad. To help you prepare for your future career, a career orientation plan is integrated throughout the programme. You can also choose to do an internship. Most of our graduates complete a master's degree. They find jobs in a variety of fields, such as education, the cultural sector, journalism, government or in communication and marketing. Are you interested in contemporary media and culture? And do you enjoy delving into questions about politics, social interaction, communities and identity? Then this programme might be perfect for you.


Okay, let's start. Okay, good morning everyone. Welcome to our session. Today we're going to show you a real use case in telecom which is using water to do energy and resource cost of the death center. So my name is Yimong Bao. I'm from China. I work for DT Corporation. And this is Alex, he's from Russia and he works for Cervodica. And let's get started. And the first thing we will introduce our problem, what kind of problem we are going to solve. And then Alex will introduce water briefly to you guys and then we will show you a real demo using water to solve this problem. And it is reported that for a death center the energy bills are typically the second largest items in their budgets. And we can see from the left chart that the first largest factor in monthly cost is the hardware cost. And then goes to the second largest one which is related to power. And you can see from the green and the yellow one. And however, it is predicted that the cost of electricity per year for a server will soon exit the cost of the hardware itself. And the reason is that servers are not efficiently used. And we say when the servers are powered on during most time they are idle and only 15 of the time they are having real workloads say having virtual machines running on them. And the most time they are idle without workload. And what's even worse, even when the servers are idle, the electricity they consume can reach a number of 16 to 19% of that active working status. And this is a very terrible problem for a death center. And this problem can be solved from different levels such as from host level we use dynamic power management. And we can also solve this from a virtualizing level such as consolidation and VM selection, load balancers, et cetera. And also we can solve this problem by consuming renewable energy resources. And OpenStack Water we provide a solution from the host level using Water when servers are left without VMs Watcher can automatically power off them or we can say turn them into sleep mode. And when the workload increase more than a given value Watcher can automatically power on them. And next I want to introduce what is Watcher for you. Yeah, hi I'm Alex and I'm a Watcher project team lead. And you know, Watcher is an optimization resource project in OpenStack infrastructure. So we leverage services provided by other projects. Mainly we have some actions like lift migrations, cold migrations, resizing power on power off actions and so on. And to apply the sections we need some sort of strategy. And the strategies, where it's from consolidation strategy to load balancing strategy, thermal strategy, noise and eyeball strategy and so on. So our main goal is to reduce the total cost of ownership across the cluster. We have the following architecture. We have three different services. Names are Watcher API, Watcher Decision Engine and Watcher Applier. And we have also Watcher Python Client and Watcher Plugin for Horizon. So we also use some metrics to generate action plan of our strategies. This metrics, we gather them from different data sources like Monaska, like pair of Nokia and Selometer. And we also have actions that connected through the API to the projects like Neutron, Nova, Cinder and so on. So let's see for our workflow. Initially we have monitoring when we gather metrics from our data sources. Then we decide and make some analysis process when if we need to stabilize our cloud somehow. And yes, if we need, then what should we do? We need to use some of our strategies. Currently we have six strategies. It's like workload stabilization using standard deviation algorithm. It's like workload consolidation when you get together virtual machines across the cluster on the as few nodes as possible. And then turning off some nodes or turning them to the ACPIS tree state. Then after we know that, yeah, okay, we need some stabilization actions, let's do audit. We launch our strategy and we get action plan result. Action plan is a set of actions that are suggested to the administrator to be applied or not to be. Yeah, so we have many contributors like Intel, Savionica, Becom, NIC, ZTE, Walmart, IBM, Turing University, Orange and AT&T. And watcher is used in NIC and Intel platform. It is also used by MIT University and by Garvert University. So let's continue. Okay, I'm going to show you, quickly show you a demo. Just open it outside of presentation. Oh yeah, okay. Oh yeah, oh sorry. So I'm going this way, I can see it. So this is an open stack cluster with three compute nodes and now we have four virtual machines, so compute eight and one on seven. And then when the VMs goes migrated or deleted, the compute seven goes idle, then watcher generate an action to power off the compute four to save energy. And then after that, when the workload increase and we need more compute or host to support our tasks and watcher will generate optimization to help. And this is our dashboard, watcher dashboard. And this is initial hypervisor. You can see from that, four VMs on compute eight and one on compute seven. And then after we delete one VMs, compute seven goes idle and then we create an audit to generate optimization action. We use audit template and then create using that audit template. The instance of audit template. Yeah, and we can, here we create a continuous audit. That means it will generate optimization actions continuously. And we can see here, we successfully generated actions of power off. That's it? No, we still have, can we? Oh yeah, here the next action, when we create more virtual machines, we might need another compute or host to support the task. And watcher will generate the actions of power on compute four automatically. Can I speed up the video? Doesn't have to. Watcher is fully documented. Watcher is fully documented and we have a wiki page and we have very active IRC channel. You can get us on OpenStack Watcher channel. So we have different repositories mainly published on GitHub. We are under big time, so we are welcome you if you want to be our contributors. So. If you have any question, just come to our channel. So thank you very much. Thank you. Thanks for your time. Come in.


The easiest way for me to get my message across is to get in the face of the American people. Since 2005, we've lost more active duty members to suicide than we have in combat. And so now we've lost 6,000 plus to suicide, and those are the active duty members. They don't count like this young Marine that came home to our hometown. What caused me to do the walk was that a young Marine came home. He had done four years in the Marine Corps, one tour in Afghanistan. He arrived home on 4 June, and we were called to bury him on 30 June. He had taken his own life, left behind a wife and a one-year-old daughter. And I had the honor of folding his flag and presenting it to his wife. The ultimate thing is I hope I save a life. One life, and it will be worth a six-month walk. That would be a gift in itself. I don't know that I'll ever know if that happens or not, but that would be the ultimate.


After having studied the concepts of chemical thermodynamics and applications of chemical thermodynamics, obviously it is very important for the students to understand whether the same thermodynamic quantities can be obtained by other means. Therefore, it is very important to understand the concepts of statistical thermodynamics. So, what is this statistical thermodynamics and what is the need for having statistical thermodynamics? Statistical thermodynamics is a link between individual molecular properties and bulk thermodynamic properties. So, what are these individual molecular properties and what are these bulk thermodynamic properties? Remember that when you studied classical thermodynamics, you were introduced pressure, temperature, enthalpy entropy, Gibbs free energy, equilibrium constant and other related thermodynamic quantities. And you were also introduced how to experimentally measure those properties. For example, in order to determine enthalpy of a reaction experimentally, there are different approaches. That approaches can be selected like calorimetry, there are different type of calorimeters available where you can measure the enthalpy change very precisely and directly. There are alternate methods also where several thermodynamic quantities can be measured. But in statistical thermodynamics, we will start talking about individual molecules, individual particles, their properties and then make a connection with the bulk thermodynamic properties. So, let us begin from the very basics. We will initially start very slowly in developing various concepts so that everything is clear. I am sure that you have gone through basics of spectroscopy and what we learnt in spectroscopy is about how the energy levels of molecules can be calculated, can be determined and related to their structures. Now having the knowledge of those energy levels, the next step is to learn how having such a knowledge can be used to account for the properties of matter in bulk. And therefore, statistical thermodynamics is introduced which as I just mentioned is linked between individual molecular properties and bulk thermodynamic properties. Now obviously, when we will start talking about the individual molecular properties and then we start connecting with the bulk thermodynamic properties, we will require some concepts, some results from quantum mechanics of individual molecules. And then when we switch over from the quantum mechanics of individual molecules to the thermodynamics of bulk samples, it will require recognizing that the latter deals with the average behavior of large number of molecules. So, when we talk about that the latter deals with the average behavior of large number of molecules. What I am talking about is that the bulk thermodynamic properties deal with the average behavior of large number of molecules. Let us go into a little bit more details of this. So, what we will do is we will introduce statistical thermodynamics in two stages. What are those stages? First the derivation of Boltzmann distribution for individual particles which may be of restricted appellate building, but it certainly has the advantage of taking us directly to a result of central importance in a straightforward and elementary way. As I mentioned that we will develop the concepts in a very simple manner and then what we will do is we will extend the arguments to systems which are composed of interacting particles. Keeping these in mind and having a knowledge from spectroscopy that there are different energy state, there are different energy levels. Let us now start discussing about the distribution of molecular states. So, now let us start discussing about the distribution of molecular states. Let us consider a closed system which is composed of n molecules. We understand what is a closed system from the definition which was introduced in classical thermodynamics. There are n molecules and let us say the total energy of this system which is composed of n molecules is E. Total energy is E. There are n molecules. It is not possible to define about how that energy is shared between molecules because the molecules if we consider the gas molecules those molecules are colliding exchanging energy and we cannot pinpoint that which molecule has how much energy. Because these molecules are continuously colliding and they are exchanging energies. The energy is not only distributed or redistributed between the colliding molecules, but it is also shared between different modes of motion. What are those different modes of motion? To say a few translational, rotational, vibrational there can be many others. So, therefore that is why this statement is made that although the total energy is constant at E, it is not possible to be definite about how that energy is shared between the molecules. As I just discussed, collisions result in the ceaseless redistribution of energy not only between the molecules, but also among different modes of motion. So, therefore, what can we do under such circumstances. If we cannot tell that a particular given molecule has this much energy, the closest what we can come is to a description of distribution of energy in terms of population of a state. And what is that population is the average number of molecules that occupy it and to say that on the average there are Ni molecules in a state of energy EI. There are different energy states and depending upon the temperature there will be different occupancy of these energy states. At the most what we can do is that let us say there are N0 number of molecules in a state of energy E0, N1 number of molecules in a state of energy E1, N2 number of molecules in a state of energy E2. And this way we can generalize that in terms of population of a state, we can specify that on the average there are Ni molecules in a state of energy EI. Consider a gas which is enclosed in a container, this gas has several molecules. The pressure which is exerted by the gas on the walls of the container, how do we define that pressure? The pressure will be equal to let me write here pressure is equal to force per unit area. How much the force is exerted by the molecules per unit area that will form the pressure, but then you cannot specifically pinpoint that which particular molecule is constituted to how much pressure and we talk about the average quantity over there. Therefore, pressure becomes an average quantity. So, therefore, we talk in terms of here average number of molecules even when we talk about population of state. Now, these population of states, these population of states remain almost constant at a given temperature, but the precise identities of the molecules in each state may change at every collision. It is very important to understand this particular concept. As I said that the molecules of the gas they are colliding with each other and how fast they collide, this will depend upon the temperature. And that is why the statement that the population of the states remain almost constant at a given temperature, but since the molecules are colliding with each other, they are exchanging their energies. Therefore, the precise identities of the molecules in each state may change. It is like saying that when a certain number of molecules are occupying a given energy state, those molecules are not imprisoned. Those particular molecules are not imprisoned in that state. The residents may change, but the average number of molecules in each state that will remain constant that is the meaning of that. And what I just talked about in terms of for example, here pressure I was talking about force per unit area. There are so many molecules which are colliding the walls of the container and we cannot pinpoint that which molecule is contributing how much force how much pressure. We talk about the average quantities. In statistical thermodynamics, we will start connecting with individual particles, individual atoms if we are considering a system of atoms or individual molecules if we are considering a system consisting of molecules. So, what we will do? We will calculate the population of states for any type of molecules in any mode of motion, whether it is translation, whether it is rotation or vibration, any temperature. We will start developing equations, we will start developing concepts and understand how to calculate the population of the states. This is important to recognize that the restriction that we will apply in the beginning is that the molecules should be independent in the sense that the total energy of the system is sum of their individual energy. This should be very clear. When I say that the molecules should be independent, let us say there are total n number of molecules in the system, then n 0, n 1, n 2, n 3 etcetera all these molecules are independent. So, that the total energy of the system is equal to the sum of the energy possessed by each individual independent particle or molecule. That means, at this point we are not permitting the molecules to interact with each other. Remember the difference between ideal gas and a non-ideal gas. In an ideal gas, the molecules do not interact with each other, but in a non-ideal gas the molecules interact with each other. And if the molecules start interacting with each other, they will interact which will lead to either release of energy or absorption of energy. Therefore, the total energy of the system will also consist of those contributions. Therefore, to begin with we will apply we will put this restriction that the molecules should be independent and in the sense that the total energy of the system is a sum of their individual energies. Later on when we build upon other concepts in statistical thermodynamics, we will permit the molecules to interact with each other and the corresponding changes will be or modifications will be discussed. So, this is what I was talking to you that we are discounting at this stage the possibility that in a real system a contribution to the total energy may arise from interaction between molecules. And obviously, the interaction between molecules will arise if there are functionalities in the molecules, there are groups in the molecules which can lead these molecules to either associate undergo the interactions which bring them together or there could be repelling interactions. It could be exothermic, it could be endothermic. So, let us forget that the molecules can interact at this point and therefore, stick to the restriction that the molecules are independent. We also adopt the principle of equal a priori probabilities, the assumption that all possibilities for the distribution of energy are equally probable. See whenever we start building some concepts, some theories we always list down some postulates that my developed theory, my developed equations will be valid if these postulates are followed. And that is why I have been discussing with you that what are the restrictions that we are imposing at this time. So, that the equations that we develop soon are under those restrictions. Now, let us start talking about configurations and weights, there are n number of molecule, we started with that there are n number of molecule. There is energy we talk about the system E is the energy. So, therefore, any individual molecule may exist in energy states E 0, E 1 etcetera. As we just discussed that in spectroscopy you learned that there can be different energy states. There can be different energy levels. The occupancy of those states, those levels will depend upon the temperature amongst other factors. And when there are large number of molecules in a given system depending upon the conditions and individual molecule may exist in any of the states E 0, E 1 etcetera etcetera. Let us keep in mind and we shall always take E 0 this one as the lowest state. Now, listen to me carefully what I am going to say for the sake of convenience and for the sake of simplicity let this lowest state be termed as 0 of the energy E 0 is equal to 0. I repeat that any individual molecule may exist in states with energies E 0, E 1 etcetera etcetera etcetera. What we will do is we will set this E 0 equal to 0 and then measure all other energies relative to that state. So, when you have a set of energy levels treat the lowest as 0 is it always 0? It may not be always 0 because you know that the oscillators they have 0 point vibrational energy. So, that that means, if we set the lowest state as 0 of energy then in order to determine the internal energy of a system we have to add a constant which is equal to the 0 point energy. Now, what is internal energy? It is important to redefine here what is internal energy. Internal energy of a system is equal to the sum of or the total energy added up in all the forms that is the internal energy. Once again internal energy is the total energy of the system added up in all the forms like if a molecule has translational degree of freedom, rotational degree of freedom, vibrational degree of freedom, electronic degree of freedom, any other degree of freedom add up energy possessed by the molecule in all the form and that is equal to its internal energy. And if we set the lowest energy equal to 0 as I mentioned over here then 0 is to be added to the total energy to calculate internal energy. Otherwise whatever is the value at E 0 that constant is to be added to obtain internal energy from the total energy. So, that is why this comment that to obtain the actual internal energy U we may have to add a constant to the calculated energy of the system. And the example that I took that if we are considering the vibrational contribution to the internal energy then we must add the total 0 point energy of any oscillators in the sample. So, what we have done so far is introduced what is statistical thermodynamics and what is the need of studying statistical thermodynamics. We want to establish a link between the individual molecular properties with the bulk thermodynamic properties. And in order to develop various formulations various equations and in order to move further we will require some knowledge of spectroscopy. We will also require some knowledge of quantum mechanics and then we will take those concepts and connect with the bulk thermodynamic properties. We also discussed some sort of essential kind of postulates which will be followed before we derive certain equations. And I hope that the basic information that I shared with you in this lecture will be helpful in understanding developing further concepts which we will now discuss in the next lecture. Thank you very much.


There are a few tech products I bought this year and when I really think about it, I probably shouldn't have even bought them in the first place. And in this video I wanted to share the five tech products I regret buying. And look, I know these may be hot takes, but they're based off of my own personal use and experience. Starting off with the Amazon Halo. Now we all know that Amazon and Jeff Bezos are trying to take over the world. They own Whole Foods. They have their own clothing brands. They bought freaking MGM. I am inevitable. But Health, that's the one area that I think they need a bit more work on. Amazon launched their first iteration of their fitness tracker, the Amazon Halo, in August of 2020. And they were trying to target that group of people like you and me, who are really looking to fitness trackers like Fitbit and Garmin during the middle of the pandemic. It was cheaper than the other popular brands. It had a minimal design and form factor. And it also tracked everything that other competitors did in regards to your health stats. But even more with their movement health, where it gave you a movement quality score and exercise plan to help you focus on improving your level of mobility.  And it had this feature called tone analysis, which would make you aware of how you sound when you talk to other people. It's just as weird as it sounds. And yeah, all of those features sound great in theory, but in execution, the original Amazon Halo was definitely not worth it, in my opinion. The app, which is the only way to access your data because there's no screen on the actual Amazon Halo itself, it wasn't reliable as many of the other apps that are out there in terms of syncing throughout the day and providing consistent health stats. And the workout program content they provided just wasn't doing it for me in terms of difficulty, quality, or interest. Honestly guys, I stopped using my Amazon Halo months ago. It's like Amazon had all the best intentions, but there still clearly needs to be more refinement on the software and hardware front. Now I also know they launched an updated tracker in late 2021 called the Halo View, which added the screen and updated capabilities, such as SPO2 and heart rate monitoring. They've also had two years to update the app and fine tune the hardware. So you know what? They might have fixed many of these issues recently, but the first impression definitely left a bad taste in my mouth and I'm a bit hesitant to reconsider. But if you're interested in me revisiting the Amazon Fitness Ecosystem and testing out its latest Amazon Halo View, let me know in the comments below. Now the next product I regretted buying, which I don't have here because I returned it, was the Peloton Guide. Now I love my Peloton bike like I really do. I even made a video reviewing why I thought it was worth the money that I paid for it, which is one of the reasons why I was so excited to try out the Peloton Guide in the first place when it was announced in early April of 2022. It was Peloton's first hardware attempt at focusing on the strength side of training and I bought the entire package, including the two 25-pound Peloton dumbbells and their branded workout mat. And at first, I loved it. It was a really cool concept. It had an Apple TV-like experience where you can navigate through with various strength training classes on your TV screen. The Peloton Guide camera would allow you to see yourself alongside the instructor to make sure that your form was correct and it could also track your various reps as you go through the workout class. The TV app would also show you the different body parts that you've trained the most so you could focus on the areas that weren't maybe getting the same type of love in future workouts. But for me, the problem was that the value just wasn't enough for me to stick to the strength sessions hosted on the platform on a consistent basis. I didn't feel that my body was getting as much work in as I did when I went to my local neighborhood gym where I had a full set of equipment. It also seemed that I was building way more muscle endurance than actual strength and size, which of course is a more personal preference for me, but I also couldn't find a seamless way to do the bike boot camp workouts. You would think that you'd be able to get off the bike and then easily transition to the strength part of the workout with the pallet time guide, but that functionality was not possible so I had to stick to just one or the other, which was pretty disappointing. I ultimately just found myself more drawn to do the pallet time bike workouts for cardio and then I just supplement my other days with weightlifting at my actual gym. So do I think it's a terrible product? No, not at all. It just isn't the right product for me. If you're just starting out on your fitness journey or maybe trying to get back into working out, then I actually do think it is worth considering as I think strength training sometimes gets the short end of the stick when it comes to people trying to lose weight and get fit when I actually believe it's the main ingredient to building a healthier body. The third product I regret buying is the TheraBody Wave Duo. Now it actually is a useful product but I think mainly for a niche purpose. The form factor is very different from your average foam roller with a peanut shaped design. You're able to foam roll those tight muscles located on your back without putting too much pressure or vibration on actual bone. It also does this without too much noise. I personally love using it on my calves, low back and traps and the five different speeds were definitely useful in determining a manageable massage level. However, I really do wish that I just bought a full size electric foam roller in the first place as this just isn't the same as using something like a TheraBody Wave Roller or the Hyperize Viper 3 where I can cover so much more surface area like my quads and my hamstrings. I just found the Duo just a bit too small of a device sometimes for what I needed it for and I feel like it just takes a lot longer for me to fully roll them up or cool down my intended muscle groups using this device. The fourth product I regret buying was the Beat Studio Buds. Now, for these, it wasn't because they were bad headphones. I actually really enjoyed using them when I first purchased them. I just bought them right before the Beat's Fit Pro came out. They have okay noise cancellation, a decent battery life of eight hours of listening time and it supports Apple's patented spatial audio. But it doesn't match the quality and functionality of the Beat's Fit Pro, which have the wing tips that allow for the earbuds to stay in your ears more securely. They also have the H1 chip which allows for haze serial activation and audio sharing. However, I do recommend the Beat Studio Buds for people who are looking for those cheaper earbuds that still have decent quality. And then I recommend the Beat's Fit Pros for those more serious workout enthusiasts and if you do hardcore workouts. The last and final piece of tech I regret buying was actually the subscription to the Headspace app. It's kind of embarrassing because the reason why I regret paying for that year membership was the fact that I just never used it. I could probably count on my fingers the number of times I actually did one of their meditations. I just wasn't hooked to it like I was the calm app. It seemed that in order to get the most out of their programs, I'd have to meditate between four to six times a day which even though that's not a bad habit to get into, I just don't personally think I have the time in my current schedule to fit that in. I specifically love the calm app because I just do my daily routine where I'd wake up, meditate for five to 10 minutes in the morning, then do a daily movement stretching, fill out my gratitude reflection journal and then be on the go for the rest of my day. And I also think that I got so used to the voices on the calm app that the ones in Headspace this just didn't do it for me. I know I should probably give Headspace a fair chance but I think I might just go back to the calm app. Now don't worry, I will definitely make another video soon on my actual favorite tech products that I purchased this past year that I do think are worth looking into. But in the meantime, check this video out which may be helpful if you're interested in other tech products that can help improve your health and fitness. Stay healthy, be happy and embrace the hype. Woo!


One of the things you discussed is this notion of amputation. So as technology gives us a capability, we then amputate the capability we used to have. You know, we've lost that ability like local knowledge to me seems to be something that we are losing. What do we need to make sure that we're not amputating? Because having GPS is wonderful, but if I don't have that, I still need to know how to navigate. And that skill of actually knowing how to use a map, is that okay to lose? Well, I think there's some things that are okay to lose and other ones are not. For example, if we were to never drive a car again, Germans would say that's terrible, right? But everybody else would say, hey, you know, well, it's kind of fun to drive a car sometimes. But if we lose that, not a big deal. But to give up giving birth, for example, in which people are proposing that we can have children outside in an artificial womb, that's not a joke.  But people are proposing that. That is a ludicrous idea. So basically we have to say, what makes us human? And driving a car does not make us human. But finding our way, I think that some of that we should retain, and then there's actually a job called the be wilder, which makes people wild again. So you go into the forest and you figure out how to tap back into those things that you still have. But what bothers me most there is that we may be the last generation of people that actually knows what offline actually means. True. That's an interesting concept. You know, 15 year old kids are always online. And so I think that we have to go back and make a conscious effort of saying, you know, you should know how to speak to a person. You should have those skills. You should be able to write, for example, there's also people saying, yeah, why do our kids learn how to hand write? Because they can speak to computer, right? I mean, every psychologist knows that if you don't learn how to write, you're going to not turn out so well. You're going to not express yourself, right? Well, that has other side effects, right? So we have to define what those things are and what we want to drop, what we not want to drop. And now technology is coming to us and saying, well, let's transcend humanity. Leave all that baggage behind so we can live forever and be superhuman. And to which I would say that's probably not superhuman. That's probably a downgrade, not an upgrade.


Hello, my name is Taz, Anthony Tascall, I'm the CIM course director for the Introduction to Behavioral Economics course. So, if you've ever wondered why we don't think the way we think we think, if you're interested in applying emotions to your brand, your marketing, your comms, if you've heard about terms like priming and framing and heuristics, but you don't really understand them, and if you want a bit more clarity about system one versus system two, come along to the next CIM Behavioral Economics course.


When the narcissist realizes you have won, when the narcissist realizes that you have become successful or victorious in their contest or conflict, everything is a game to the narcissist, everything is a competition and they have a dualistic mentality. They see everything in black or white where something is either good or bad.  There is nothing in between. It may look like they are trying to win, but they are actually just trying not to lose.  Every action of behavior they engage in demonstrates that they are losers. They do everything they can to make it look like they're not losing, but the truth is they are failing at everything they participate in because they're disadvantaged. There are often in unfavorable circumstances where they lack financial and social opportunities. They lack the basic resources and conditions that one would need to succeed and that gives them this losing mentality where they are constantly afraid. It makes them feel like they need to control everything in their environment because naturally they would never be able to succeed. They would never be able to accomplish anything because they lack the capabilities and potential to achieve anything on their own. It causes them to lose confidence in themselves. It causes them to feel powerless and people who feel powerless will seek power. They will seek the ability to direct and influence people's behavior at the course of events. They will try to control you. They will try to maintain influence and authority over you to compensate for their lack of confidence, ability and power. This is why everything becomes a game with a narcissist. This is why everything becomes a competition, but it's not because they are trying to win. They are trying not to lose. They don't want to be seen as the losers that they actually are. Even though every action and behavior they engage in demonstrates that they are losers. They will manipulate you. They will try to deceive you. They will cheat, lie and steal. All in an attempt to avoid looking like the losers they actually are.  And it's that feeling they are trying to avoid. Which is why they are desperately seeking power and control. They want to control the narrative so that they can control how they feel about themselves. And that is why everything becomes a competition. That is why they are constantly trying to compete with you. But it is never a fair contest. The game is always rigged in their favor. They are always covering all bases. They will deal with everyone and everything. They will prepare and anticipate for every possibility. They will give attention to every aspect of a situation or problem. They will inform people of all matters at hand. All in an attempt to manage the risk of them losing. Because they already know that they lack the capabilities and potential to succeed. They will go to great lengths to reduce that risk. To the point where it becomes an obsession. To the point where their entire lives become a competition. Full of unwilling or unknowing participants. When you have won against the narcissist. It's really humiliating to them. It makes them feel ashamed and foolish. It mortifies them. Because while you may have been competing on your own. In most situations the narcissist will have had a team of flying monkeys assisting them. They will have handicapped you in some way. They will have tried to level a playing field.  Making it almost impossible for you to win. But when you do win.  Because they had all of these people against you. They covered all bases and did everything in their power to crush you. And yet you still came out on top. You were still more successful than all of them put together. Which really makes them feel small. It makes them feel completely worthless. Because even with all of them combined. It still wasn't enough to defeat you. You still managed to win.  You endured the disabling conditions that they imposed upon you. And still managed to surpass what they had achieved. It's like you were running a race. And at the start of the race. They placed a ball and chain around your ankle to hold you back. But you still won the race. You still defeated them.  Because if they were even a fraction of what you are. They would have defeated you. When the narcissist is placing limitations on you. They're more focused on your results. Rather than what they're doing to you. They look at it as though those are your actual results. Rather than it being an effect of their limitations or abuse. But when you succeed. Despite what they're doing to you. They have to see it. There's no other way. They will realize that you have won. The narcissist may realize that you have won. But that doesn't mean that they are going to like it. That doesn't mean that they're going to accept it. They will do everything they can to try to sabotage everything you have achieved. They will try to take it away from you. They will try to smear your name or discredit you. They're not just going to accept that you have defeated them. They are sole losers. They will become very angry and upset when they lose. They will even complain and blame you for their loss. They will say that you are responsible for them's fortune. And they may even expect compensation from you. If that doesn't work. They will try to minimize your success. They will represent or estimate it at less than its true value or importance. They will act like it isn't that great. Or they will say that you're not deserving of what you have achieved. They will try to discredit you. They will try to harm your reputation because they cannot stand to see that you have won. They hate it. It just reminds them of what they are. It reminds them that they're losers. Everything they do is an attempt to regulate their emotions. They control you because they're trying to control their emotions. They want to keep you down or hold you back. Because it makes them feel better. When they see you getting ahead. It just reminds them of how small they actually are. And they're doing everything they can to avoid reflecting on that fact. Deep down they know that they are losers. They just don't want to be reminded of it. They would rather exist in this fantasy world where they are the winners. Where they have defeated you. Even though they know that's not true. They will just pretend. They will entertain the land of make-believe. Because reality is just too painful for them to deal with. So rather than focusing on your success. They will focus on your faults and mistakes. They will focus on your flaws and imperfections. They will focus on trying to tear you down. Anything to avoid having to entertain the fact that you have won. Even though they know that you have won. They just don't want to acknowledge it. They don't want to accept or admit the existence or truth of that. Because it's too painful for them to deal with. It makes them feel small. It reminds them that they have lost. They think that by trying to sabotage you. Or take away your success that they are winning. When the definition of a loser is someone who has caused a loss.  And they are disadvantaged. Which is why they are constantly trying to gain an advantage over you. Because in their minds it's not fair. In their minds you have an unfair advantage. You have a condition or circumstance that puts you in a favourable or superior position. And that is why they are always trying to handicap you. They are always trying to make your progress or success difficult. They are always trying to create hindrances or obstructions. They are always trying to create things that provide resistance or delay to you. Because they are trying to slow you down. So that they can get ahead. They cannot play fair. Because they believe that you have an unfair advantage. And that is why you will often be competing against a large group of people. Rather than one other person. That is why they will prepare and anticipate for every possibility. That is why they will give attention to every aspect of a situational problem. And they will inform people of all matters at hand. Because they are terrified of losing. They are terrified of being seen as the losers that they actually are. They don't like how that feels. Which is why they are constantly trying to project those emotions onto you. They do everything in their power to avoid looking like the losers they actually are.   A winner just goes straight for the win. But narcissists do not have a winner's mindset. They have a losers mentality. Which is why they will continue to spend the rest of their lives trying to cut corners in an attempt to get ahead. But when they cut corners all they end up doing is going around in circles. Going nowhere. They just repeat the same things again and again. But it never gets some of the results that they are looking for. But they are not even aware of that because they are just trying not to lose. And that is why most of these people never really amount to anything. Rather than doing what needs to be done. They are more focused on managing your perception. Making you think that they are winning. But it never gets them anywhere. Because all of their efforts go into the orchestration rather than building something for real. They are more focused on just trying to fool you. They would rather skip the hard work and just go straight to getting their reactions to their illusions of success. Because your reactions make them feel good. It makes them feel like in that moment. Maybe they are not losers after all. Thank you for watching. I hope this video has an interview. Please like, comment, share and subscribe. Click the bell icon to receive notifications for my future videos. Check out the new Narc Survival website at www.narcsurvival.uk Where you can read my blog posts, book coaching sessions and join a support forum.


So, I think we know that in today's world we're facing several existential crises, climate change, biodiversity loss, and what I think IID brings to that is a very people-centered set of solutions. So, the only way we can solve the climate crisis at Preserver and Biodiversity and have greater equality is by looking at how people fit into all of the different ways that we live life. And I think that's what IID's action-oriented, people-centered research can bring to the world. In what way do human beings fit in this natural environment that we want to look after differently? I think we need to make the greatest change in the world by looking at what we value. I think in the last four or five decades we've come to value the wrong things. We value buying things and throwing them away. So I think looking at how IID values markets, values people's knowledge, values local knowledge, our natural resources, and looking at how that can shape more sustainable solutions and more sustainable ways of living on earth is going to be really important. And luckily that sits and absolutely fundamentally reflects the values that our IID itself.


Today we're going to be looking at using the bootstrap to create ARM images for devices such as Pogo plugs or to get Debian running in a churroot on your Android device. If you enjoy my tutorials and would like to see more, please think about contributing to my Patreon account at patreon.com forward slash metal x 1000. Okay, we're going to be creating an image that will contain an ARM file system for use on different ARM devices and that can be churrooted into an Android device or any Linux device that you have root access to that is ARM based. Okay, so here we go. I am in a folder. It's an empty folder. There's nothing in here. I'm going to create a folder in here. I'm just going to call it MNT. We're going to create the image first that I'm going to mount it to that folder we just created called MNT. So I'm going to use... there's different techniques to create file images. I'm just going to use DD. Again, just like last tutorial, pretty much everything I'm going to do in this tutorial requires sudo or root access. So I'm just logged in as root on my system. Some people frown upon that. If you prefer, just put sudo before most of the commands. So I'm going to say DD. I'll give it a bs of 512. I'm assuming that you're somewhat familiar with the DD command. But what we're going to do here is give it a count. So if we don't give it a count, it's just going to keep creating an image that goes on and on and on and on. And we're going to say 5400 looking at my notes. And I have that written down as approximately a 2 gig file. There might be another way to write that out. That's easier to remember, but that's what I have on my notes. So now we're going to give it an in file. So this is information we're going to put into the image. We don't want to put really any real image information in there. So we're just going to use the device zero. This is going to fill the image with a bunch of zeros. And then we're going to say out, our of out file equals, and whatever we want to name the image, I'll call it Debian underscore arms so that I know it's an arm image.img. I'll hit enter, give it a few seconds here. Hopefully shouldn't take too long. And we will have a 2 gig image approximately, which we then will have to format and mount.  So yeah, well, a little bigger than I thought, 2.8 gigs. So almost three gigs. So you can tweak this number somewhat. That gives us enough room for the file system and room to do install the software that we want on there. So now I'm going to use MKFS.ext4 because I want to make it ext4 file system. And I'm going to point it at that image. We're not creating, so right here it's telling us there's no block special device. That's because we didn't create a partition. The whole image is going to be a partition. Depending on what you're doing, and I've gone over this in previous tutorials, you may or may not want partitions in there. We don't want, you know, separate partitions. We just want to write to, like if you think of this image as a hard drive, we're writing directly to the hard drive without any permissions or partitions. Okay, so now we can mount it. Mount. And again, don't forget I'm running as root. If you're not, you have to put sudo before these commands. I'm going to dash o loop. We're going to loop back to the image. The image is called debianoscore and arm.img. And where do I want to mount it? I'm just going to mount it in the folder. I just created the beginning of the tutorial called MNT. It is in the current folder. If I list what is inside that folder, it just has the lost and found folder which has to do with ext and how it writes to the files. Another tutorial talking about that. Okay, so at this point, there's a few things that I'm going to want to install. I'm going to want to install the bootstrap, which I already have installed. And a few other tools for once it's done being installed, which I'll explain more about momentarily, or once after we do our install, I'm going to say aptitude or apt get, whatever you use, install bin FMT dash support, QMU, which is an emulator, and then QMU dash, user dash static. And then if you don't already have installed the bootstrap as well, which I do have installed, in fact, I probably might have this stuff installed. Yeah, looks like I already have all that stuff installed because I've done this before. Okay, so now what I'm going to do is I'm going to use the bootstrap similar to what we did in a previous tutorial, the bootstrap. But since we're not using, you know, a regular 32 bit or 64 bit, you know, standard desktop processor, I'm going to say, foreign dash dash. And let's tell it I want to do an architecture of RML. Now the version of Debian I want to install, I'm just going to do Sid, which is unstable, depending on what you're using is for you may want Sid, you may want Wheezy, Lenny's the old stable, I've been using unstable for so long, I've been using Sid, I don't even know what other versions are at. But I'm going to say Sid, where I want to install to MNT the folder that is within the folder we're in. And then you can tell it what server you want to install from. If you leave a blanket should just use the default Debian servers and it is. So it's going to Debian.org. And it's going there and it's going, ah, okay, he wants to do a the bootstrap install of Sid, but he wants an arm. So it redirects me to the right folder and it starts downloading all these packages. Just like the last tutorial I'll try to talk here while this is downloading. I may pause the video since this will probably take a little bit. Again, right now we're doing, we're downloading all these files to this folder MNT, not in the root directory, but within the folder we're in that we just created. Again, that's what we created. It may be called something else. But which that is actually the image because we mounted our image to that folder. So right now it's putting all these files, all these minimal tools that the Debian system needs to run. And actually there's ways to make it even more minimal. But we'll consider this minimal for now. Into this image, at which point we can churrood into an arm system. Now I should also mention there's two ways of doing this. I like doing it this way.  Most instructions will tell you to do a two-stage install where you start, it pulls down the files, but then you load that file onto an arm device and then start doing whatever you need to do from there. It does the rest of the install with the second stage. What I'm doing it here is I'm pulling down all the stuff, all the arm files, which obviously can't run on my processor, on my desktop here because I don't have an arm processor. But that is why we installed QMU and those other, I pronounce it QMU. I'm not sure if that's really how you pronounce it. It's Q-E-M-U, which is a virtual machine that supports different architectures. I've gone over it before in the past where we actually did an arm install using it using the Debian net CD. So we're kind of doing the same thing here but without that CD and actually without needing QMU to pull down the file system. But what I'm going to do is I'm going to go into the, I'm going to churroot into it which would normally not work, but I'm going to show you how you can access an arm file system from a regular processor right now. There are some long commands that I am going to mostly copy and paste, but I'll put them in a link in the description so that you can have those. So we did that. Okay, so now I'm going to say copy from my current system, the USR bin folder, the QMU-arm-static file that we installed. And I'm going to copy that into the new file system we just created underneath MNT, USR bin. Boom, so we put that there. Now we're going to set some settings on our system so that when we churroot into that, it's going to use that emulator that's in that image so that we can actually run stuff in the churroot even though it's an arm system on our, this is a 64-bit AMD processor. So this is what we're going to type. And I'm going to do some copy and pasting. So case sensitive here, Debian frontend equals non-interactive. Then we're going to say debconfig non-interactive seen true. And then we're going to say lcall equals c, language equals c, lang equals c. Again, this is all I got off the internet a while ago. I'm not even sure what a lot of this means. Then we're going to put in our churroot command, the directory where our debutstrap was installed to. And then we're going to say debutstrap, debutstrap dash dash second dash stage. And I'm going to hit enter. And I got a failed. Fail to run command. No such directory. I spell everything right. Nope, I did not. I think there's needs to be a T there. debutstrap. There we go. So as I was saying, we did the first stage of installation. Most tools will tell you to do that. Then load this file system onto an ARM device and continue the second stage there. One, I like to do everything on my desktop when I can. Two, I'm just going to assume that it's faster doing it this way because my desktop's faster than, let's say, my phone. So what we had to do to do that was just install QMU, copy the file over, and then add in these settings here, which again will be in a link in the description of this video. Okay, so now it's doing the second stage. Before it pulled down files, now it's actually doing its churrooting in and doing the second stage install. At this point, I'm going to pause the video, and we will continue from there because this will probably take a little while for it to unpackage everything. Okay, that took a couple of minutes, probably around five minutes, probably a little bit less.  Now we're going to do another command similar. So I'm going to hit up arrow because it's all the same up until this last part here. We already did the second stage, and this time when we churroot into the thing, we're going to say dpkg-dash-configure-a. Okay, so now that we've done that, we should be able to churroot into the system. So let's do churroot, the folder that we want to churroot into, and I'm pretty sure if I type just bash, it's not going to work. Oh, also if we type churroot correctly. Oh, it did work. Okay, so let's see. Let's think of a command. Let's do aptitude, get aptitude install. Well, let's check something before I try running that. catetc-apt-source-list. Notice there's nothing in there. So what we want to do is add the server that we want to download from, and let me just see. I think that we should just be able to do one. I think nano will be installed by default. And in here, let's say debhttp, forward slash forward slash, I think it's ftp.debian.org, forward slash, I think it's debian, Sid main, I think. I'll give that a try, otherwise I have to look at my notes. Now if we do aptitude update, we'll see if that's correct. Yep, seems to be working. And it knows based on our system that we are an ARM system, so it's going to download the repository list for ARM. But at this point I could do aptitude install nmap. And it'll download install nmap. Now remember, everything I'm doing right here is being done on an ARM file system. And it's made possible to churroot into an ARM file system with this debootstrap install because we did the QMU. Again, I don't know if I'm pronouncing that right. QEMU, emulator file, and we copied that over so that when we churroot into it, the churroot knows to use that so that we can run these ARM programs on a non-arm processor. So right now, again, we're working with inside the image we created, install whatever packages you think you want on your phone, and then you can copy this to your SD card, or if you have enough storage on the memory on the phone, you can do that. You can mount it. And if you have root access, you can mount it. And then you can use, if you have a full version of busybox on there, if not, lots of times a lot of Android devices have a slimmed down version of busybox. You'll have to get the full version, which you can find online, which has churroot built into it. You churroot into this Debian image after mounting it, and you'll have a full running Debian system on your phone. And obviously, you can't run the standard GUI applications in the Android interface, but there are ways to kill the Android Zygote, which is the process that starts the Android interface. You can kill that. And if you know about Xorg configuration files, you can configure it and actually get Xorg running. And actually, on any Android device with a little bit of tweaking and an image like this that we just created, you can have a full Debian desktop running on any Android device. The biggest drawback would be getting video drivers to work, because if you do start up Xorg, at least when I've done it on my Android devices and I have done it on both my tablets.  FrameBuffer is the way that I go for displaying Xorg, so you're not going to get any acceleration and good luck getting the touchscreen calibrated. I have not been able to really figure that out, but I have been able to get things like Mplayer and at least the desktop open and other applications open to on an Android device using the FrameBuffer, but actually having a full working desktop, I myself have not been, but that's also, I don't know very much about the Xorg configuration file, because I've only been using Linux for eight, nine years now, and pretty much my entire, you know, the last seven years at least, you don't have to touch the configuration file. Linux is so good at configuring everything for you for most hardware, so this is going to take a little while to install. There's a lot of packages required for the Nmap that where it wasn't installed yet, but that's it. Very simple, mostly similar, very similar to the previous video, but with the add a little using the QMU to be able to access that true on standard desktop. I encourage you to play around with this. I know I personally love having Debian installed on my Android device. What I normally do is I write out scripts on the Android device that automatically mount the true route and run a script and then save the output as HTML and open up Firefox. So on my phone, for example, I open up a terminal. I use connect bot and then I just I SU into route and I can type in scan and my script automatically does a double ARP scan, grabbing a range of IPs on the local network and then outputs those as HTML to a file and opens up Firefox. At that point, the script continues running in the background, doing different scans like Nmap and other network scans continuously updating the HTML file, which I then have the GUI interface as HTML that in that case I use Firefox. I have my script open up Firefox. So at that point, like it scans if it finds a server running on port 80, it gives me a link. I can click on that and the browser opens it up. Very, very convenient. I mean, a lot of which you can do with a full version of busy box, but it's nice to have the full Debian system for that sort of stuff. So I'm just going to let this go. Toriel is pretty much over. I thank you for watching. I hope you enjoyed it. Again, this video was what was voted on with my Patreon viewers. If you enjoy my tutorials and you want to support my videos, my work and my website and continue seeing videos, think about contributing to my Patreon account over at patreon.com forward slash metal X 1000. I much appreciate it. Plus, as a patron, there are different reward levels, one of which is you get to vote on what series I'm doing next. And this time around, it was voted on the bootstrap. So I've done this is the second video on the bootstrap. I've got at least one more, which is going to be a simple bootstrap through Gremel. I think it's how you pronounce. It's great, great live CD Debian based for I hate using power users, you know, but it's very lightweight and very powerful with lots of great scripts on it. So I'll probably look at that in the next tutorial. And so if you like this topic, great. If you like other topics and want to have a say, consider going to my Patreon account. And there's different levels with different amounts of input that you can give. So of course, you get stuff as well, including early access to videos and downloadable links to add free videos. So now that I've promoted myself enough, I want to say have a great day. Please visit filmsbychrist.com. That's Chris with the K. There's a link in the description. And I hope that you have a great day. It's got a 250 gig hard drive, which I love. We also have a slightly cheaper model. If you need to, at this point, you can practice this little circle with the person in it. That's accessibility things has things like on screen reader. And you can choose, you know, on screen keyboard. And there's a few options for the keyboard there. We can close that.