Let's go ahead and get started. So I thought that the first thing that I would do is go over the homework assignment for this week. We've already covered all the material that you need to know in order to do it. And hopefully it'll be fairly straightforward. Can you see this with the lights on? Okay. All right. So there are six problems. And the first one is to report how many permutations are there of 200 distinguishable objects. So that should be obvious from the notes, how to get such a number. And then the second one has to do with the binomial coefficient. So that's how many ways can you take 200 distinguishable objects and divide them into two groups, one containing 150 and the other containing 50 without regard to the order. And then the third one is a calculation similar to some of the examples we've done in class where you use essentially the binomial distribution to calculate the probability of getting 40 heads in 100 flips of a fair coin. And then in number four, what I'd like you to do is plot the probability of getting exactly M heads in 200 coin flips as a function of the number M. Okay. So again, that's an example, very similar to that in the notes. And I've advised you to use the option plot range arrow all so that you get a full plot of your function as opposed to just part of it. Okay, then number five, there's a couple of things to do. So there is on the homework web page, there's a file called chem1afinalscores.dat, it's final exam scores from a Chem 1A class and two columns of data. The first column is just a number of a student, one, two, three, four, five, et cetera. And the second one is the corresponding scores. So what I want you to do is import that file into a matrix and then I want you to report the minimum, maximum, median, mean, and standard deviation. Okay. And then make a raw histogram. So just the raw counts using a bin width of two, that's part B. And then in part C, I want you to do a couple of things. So first, make a probability density histogram from those scores and it says to use 40 bins, okay. And then you want to assign that to some variable and then make a separate plot which is a normal distribution that has the mean and standard deviation of the distribution of scores, okay. And save that plot as also a variable and then use the show command to put them on top of each other. And the thing I want you to look for here is whether or not you think the normal distribution accurately represents the distribution of scores in this particular Chem 1A class, okay. So you can make a comment about that at the end of the problem. Okay. Last problem is you're going to plot molecular orbitals, okay, using three-dimensional plotting techniques. All right. So you all remember, I'm sure, from your GCAM, the concept of molecular orbitals. So molecular orbitals is a way to describe the electronic structure in molecules and the version of the molecular orbital theory that you learn in general chemistry is the so-called LCAOMO model which stands for linear combination of atomic orbitals. So the idea is that each atom in the molecule contributes some atomic orbitals and then those go into a hat and abracadabra occurs and out of the hat comes the same number of orbitals but now distributed over the molecule. And you may recall that the way those orbitals are combined, the atomic orbitals are combined in the molecular orbitals, you end up with so-called bonding and anti-bonding combinations, okay. You could also get non-bonding combinations, okay. So what you're going to do here is you're going to plot the molecular orbitals that come from combining two hydrogen 1S orbitals into molecular orbitals for the H2 plus ion, all right. And so what you get is two molecular orbitals. One is a sigma called sigma 1S. So it has cylindrical symmetry along the bond axis and it's a bonding combination. And in Cartesian coordinates the functional form is like this. This isn't exactly it but it will give you the right shape, okay. And then there's a non-bonding or an anti-bonding combination that is the same thing except instead of adding them together we actually subtract them in the two terms, okay. So these are basically just S orbital-like functions. All right and here D is the bond length and the units here in Bohr radius but you don't need to worry about that. Okay so I want you to use D equal 2.5 and then make separate plots of each of these functions using plot 3D and you should recognize them because you've seen them in your general chemistry textbooks or you should have anyway. All right now so that's part A and I tell you what range is to plot the functions over in plot 3D and then I want you in parts B and C to make contour plots and density plots of not the orbitals themselves but their squares which are proportional to the probability density of finding the electron at a particular region space and there's slightly different ranges here. And in part C for the density plot I ask you to change the color scheme to gray tones. Okay so that's the homework for this week. Does anybody have any questions on that? No. Okay well so we're going to continue today with plotting and I want to just quickly summarize what we've done so far in terms of plotting. Okay so we have plotted functions or data of the form Y equals F of X. So here we have a single independent variable here. This gives us a two-dimensional plot and we've seen how to do this with the plot command and also the list plot command for discrete data. Okay and then more recently we learned how to plot three-dimensional functions of two variables and we have three ways of doing that which you will explore in the homework. So one is plot 3D and then we also have contour plot and density plot. Okay now today to finish up our plotting we're going to learn how to represent at least partially functions that have this form. So how many dimensions is this function or surface S going to be? One variable, two dimensions, two variables, three dimensions, three variables, four dimensions. It's not a trick question. Okay now I see you're kind of wondering well how are we going to do that? Can anybody see in four dimensions? If you can you're unique. How about do they make four-dimensional glasses like they do for three-dimensional movies? Well so then this is a little strange right because you've certainly seen depictions of functions like this. How many dimensions does an electron in an atom move in? Three. And then how is it that we can depict an orbital in a textbook? You've all seen the pictures right? There's pictures of orbitals. So you're seeing a representation of a four-dimensional function but what you're actually seeing see is a contour plot. So remember when we could plot three-dimensional functions in two different ways right? We can display the whole three-dimensional surface or we can make a two-dimensional plot of a three-dimensional function by drawing its contours. So that's the trick to seeing a picture of say an orbital which is a four-dimensional function represented as a three-dimensional object. It's actually a contour plot which you look at when you see those pictures. Okay and there is a command in Mathematica which we're going to use and we'll use it to visualize atomic orbitals which is called contour plot 3D. Now so what are we actually going to draw with that? Well like I said we're going to draw atomic orbitals. Okay so those of you who are taking PKEM right now you're learning how to solve the Schrodinger equation and pretty soon you'll talk about how that's done for the electron, the problem of the electron in the hydrogen atom and you'll see the hydrogen like orbitals emerging from that. And you'll find that using say X, Y and Z is not the most convenient set of coordinates for solving that problem. Okay you're going to find that it's the distance from the nucleus as well as a couple of angles. And so the functions that you're going to be looking at are going to be functions of r, theta and phi, r being the distance and theta and phi being two angles. Now once you have those orbitals you can write down Cartesian versions of them. So Cartesian coordinates are X, Y and Z. And that's what we're actually going to plot here so that we don't have to worry about all the special functions that arise in the case of r, theta and phi. Okay so we're going to write orbital like functions and you'll see they have more or less the correct shapes so orbital like functions they're going to be functions of the Cartesian coordinates and they're going to be in the following form a constant which we'll ignore times a function G of R and H of X, Y and Z. Okay and R here is the distance measured from the origin which is X squared plus Y squared plus Z squared square root. Okay and the functions that we're going to consider today as examples are as follows. So we're going to consider something that looks like a 1S. In that case G is equal to E to minus R. This is going to be in units of Bohr radius and H is equal to 1. Okay and then we're also going to look at the 2PZ. Do you remember what the 2PZ orbital looks like? It's like a dumbbell. It has two lobes and which axis is it aligned with? Yeah. Okay so this one's going to be E to the minus R over 2 again in units of Bohr radius, the distances and H is going to be equal to Z. And then we're going to look at the 3DZ squared orbital. So you remember what that one looks like? That's the D orbital that looks somewhat like a 2P except it has the same sign in both lobes unlike the 2P. And then it has the donut around the XY plane. Okay and so for that one G is equal to E to the minus R over 3 and H is equal to 3Z squared minus R squared. Okay so these are all going to be four dimensional functions and we're going to represent them as three dimensional contour plots. All right so I think we have everything we need to get started.  All right so then once I have that I can use it over and over. Okay now for the 1S orbital then I'm going to say F of XY and Z colon equals E carat minus R of XY and Z. Now the contour plot 3D command so here it is 3D. You actually have to specify the contour level that you want your function to be drawn at. Okay and so this is going to introduce us to a new kind of equals which is the double equals sign and this is a place where yes oh I have an X instead of a Y. Thank you. That would have been a pretty funny looking thing. Thank you very much and okay so what we do then is we say what do we want to plot? Well we're going to plot F of X, Y and Z and then we need to specify the value okay now if you look at the function that we're plotting you can see that it's exponentially decreasing with R. Okay so as XY and Z get bigger and R gets bigger this function dies off exponentially and you can also see that it goes between values of 1 and then as R goes to infinity it will be 0. So the contour we choose should be a low value of the function so that we can draw you know an envelope that it encompasses you know a large amount of the function. Okay and so what I'm going to say is that I'm going to choose the value F equals to 0.1 all right so it will be 90% decayed on the contour that we're going to see. All right now to specify that we have to use double equals okay and if when you're doing these say in homework or something next week if you don't get anything it might be because you forgot the double equals. So I'm going to set it equal to 0.1 and then I have to specify the ranges of X, Y and Z and this is sometimes done by trial and error okay or if you wanted you could plug some numbers into the function and get a rough idea but anyway so for this plot X going from minus 3 to 3 and the same for Y and Z works pretty well. All right so let's go ahead and let it rip. Oops we need a minus 3 here sorry okay now one thing to notice is that there's actually a fair amount of calculation going on here because we have to evaluate the function and find out where it actually equals the contour okay anyway at the end of the day you get something that looks like a sphere centered at the origin and sure enough that's what we know the 1S orbital to actually look like okay. Now what if you wanted to see more of the function? Well you could lower the contour a bit say 0.05 what's that going to do is it's going to make the sphere bigger or smaller? Well what it means is it will be going out to R so where the function is decayed even more so it'll be a bigger surface right the smaller the value of the function the bigger the surface will be. All right see so it grew all right and if you want you can grab this guy and move it around and it's also helpful when you're drawing these to put in some axes so let's go ahead and put in axes labels and so I'll just say X, Y and Z. Oops we need a curly all right so there you have it. So now you can see in four dimensions sort of you can see a shadow in four dimensions okay the shadow of a four-dimensional function basically all right so I want to take this opportunity to show you something that some of you may have already discovered or needed to use but it does occasionally become useful when you're doing number intensive things like these contour plots because from time to time the mathematical kernel gets screwed up and it's useful to know how to stop it and restart it so that you can continue your work so sometimes if you know mathematics is not responding or you think you've put something in correctly and you're not getting a result this is something that you may try in order to make sure that it's not your code and that it's just something going on with the mathematical kernel. So the engine that underlies the program mathematics is called the kernel and the way to turn that off and restart it is as follows so you go under evaluation and you go down here to quit kernel and select local come on and then you say yes I really want to quit okay so now mathematics is dead okay and if you want to start working again you go down and say start kernel local okay and that basically fires it back up and then if you want to reevaluate your notebook you could say evaluate notebook and then it'll just go through and redo everything that you had done and that way you can see if you still have any issue you know this is something that you might want to try from time to time when you're having problems and you don't think it's anything to do with your commands okay now so this here is a beautiful 1s orbital and I imagine that a lot of you are probably a little underwhelmed at the moment so let's do the 2pz it's a little more interesting alright so let's just go ahead and mouse all this F and contour plot stuff in okay and put it back alright now we have to modify the function a little bit so first of all we'll put in the r over 2 here and just to make sure everything is done correctly we'll put this in parentheses and then we just have to multiply out in front by z okay now I think we're otherwise okay for the time being so let's go ahead and enter that and we should see in principle a 2pz orbital now that doesn't look like a 2pz orbital does it does anybody think it does okay so what's the deal well one of the deals is you remember that as the principal quantum number of the electron in the hydrogen atom increases its orbits become larger okay so one thing we could suppose is that we're only seeing a piece of the function here because 2pz orbital is bigger for a given value of the function than is a 1s so we should certainly increase the ranges over which we're looking at the function okay and so for example we might increase these values to 10 boron radii instead of 3 alright so let's try that alright still cut off but we can fix that by just putting in 0.1 instead of 0.05 so we'll see a little less of the function but you can already see that this does not look like a 2pz orbital does it so what's the deal it looks like we're only looking at half well we are only looking at half you may recall from G. Kemp or from organic chemistry where these kind of knowing something about the sign of the lobes of the orbitals one of these lobes has a positive amplitude and the other one has a negative amplitude so we're only looking at the positive one here because we specified a positive value for the contour okay if we want to see the whole thing we need to plot another surface to go with this one that corresponds to the negative the lobe with negative amplitude okay so let's we can fix that pretty easily so what we're going to do is we're going to put in a curly bracket here and we're going to plot this positive one along with a negative one that has the same contour level okay so I'm just going to put a minus sign in here and then a curly bracket okay alright so we can let that rip and now we should see a 2pz orbital okay so now there we have something that looks more like the 2pz orbital that we know and love and it's still not that pretty because we've plotted the surfaces with the same colors and so it might be informative if we're trying to explain to somebody about the signs of the lobes of the 2p orbital it might be informative to color the two lobes different colors okay so we can do that using directives as we did previously for three dimensional plots okay so what I'm going to do now is make a nicer looking plot by turning off the mesh okay so the mesh will be gone and now I'm going to specify some details of the contour style okay so for this I'm going to use directives to make these shiny surfaces with different colors for the positive lobe and the negative lobe okay so for the first one I'll say directive and I'll make this one green and then I'll change the specularity to make it a nice shiny solid looking surface so I'll say white 100 we saw this previously okay so that's for the first one and then for the second I'll do the same except I'll make it a different color okay so we'll change this say to yellow all right so the first directive applies to the positive contour surface so that'll be green the upper one and then the second directive will change the negative contour surface to yellow all right so let's see if that works aha they worked so now you have a picture that's worthy of being put into a GCAM textbook okay all right now let's do the 3DZ squared okay any questions on this so far just scroll up or down do you have the same ranges did you put e to the minus r over 2 you have the z maybe you got a Christa can check it all right any other questions yeah okay so the double equals is the way that we specify the value at which we want the contour to be drawn okay and the double equals it's just the mathematical syntax and we'll see additional uses of that later on it's sort of like saying sort of like saying making a special case right saying I want the function evaluated at that while I want to represent the function that when it's equal to precisely that value okay all right and that's a that's a source of some headaches because sometimes you forget to put that in and then it's hard to see because notice this double equals here has a very tiny little space in there that makes it hard to see that it's actually a double equals any other questions okay so let's move on to the 3DZ squared and so let's go ahead and grab all this stuff put it down here okay so now we need a slightly more complicated function so we'll say h minus r over 3 and then in front we're going to have 3 times z squared minus r of x y and z parentheses okay and we have to increase the limits because now we're moving up another principle quantum number and so I'm going to go ahead and put in 30 okay and so now we'll draw the surfaces in the same way as before the positive lobe will be or the positive part of it will be green and the negative part will be yellow crunch crunch crunch okay something looks a little weird there aha so notice it's 3Z squared minus r squared and I have only r okay so we need to fix that so this should be r of x y and z squared it will be worth the wait okay so there you have it does that look familiar more or less like I say these functions that we're plotting these are not exactly the functions describing the orbitals they're just they're close and they are giving a reasonable depiction of the shape okay so that looks kind of like the 3DZ squared and from this we can be reminded that in the in this orbital the part that's aligned along the z axis that looks a little bit like a p orbital is actually all positive amplitude and the doughnut going around it in the x y plane is negative amplitude and if you want you can change the colors easily so for example suppose we wanted to call this or paint this one red and this one blue we could do that just have to wait okay so while we're waiting I'll tell you that there's another way that we can well there are other convenient ways to depict functions such as this okay so there you have it maybe you like that better if you're feeling patriotic today okay so this is the way we draw three-dimensional contour surfaces contour plots of four-dimensional functions now you've probably also seen in your textbooks other useful representations of the orbitals drawn as contour plots but through but showing a plane cutting through the orbital so I want to show you that because those make nice looking diagrams also so this is taking the three-dimensional contour of the four-dimensional surface but we can also now take slices through this guy and look at two-dimensional representations of it so for example I could come through with a knife and carefully slice through the middle of the thing where y is equal to 0 okay and basically eliminate y from the function so that now I actually would have a function of two variables which I can represent as a three-dimensional object using say contour plot or density plot okay so let's see how we can do that all right so we'll do that with this 3z squared 3dz squared and so what I'm going to do is grab up to here actually I want the function to sorry all right so what I want to do now is represent the this orbital as a slice through the xz plane or in the xz plane so that y is gone okay so how can I do that well first of all I can define my r now as function of x and z only all right so I've removed y from the picture so that'll be square root of x squared plus z squared and now f is not a function of y anymore so we can get rid of that and get rid of it here and get rid of it here okay and now I'm going to use the regular contour plot command and plot f of x and z and I don't need to specify the contour anymore because Mathematica will choose contours for me I can use the same range and I can get rid of the y axis here and then finally put in the bracket here oh I have to get rid of the y limits here too okay so now I think we're ready to see the 3dz squared orbital in the xz plane aha oh it's not squared thank you still got a problem here oh okay that worked all right so then it's a little bit screwed up because it didn't show the whole thing so we can say plot range arrow all re enter and now you see a nice picture of the 3dz squared orbital but now slice down along the y equals zero plane so we're in the actual xz plane and I didn't get labels on my axis because I forgot like I do all the time that the contour plot is drawn with a frame so I have to say frame label okay so now you can see I have x and z okay you want more contours you can put more contours does that look familiar to anybody seen plots like that before you can see the positive lobe drawn with the lighter colors going to its maximum value at the white and then the negative lobe drawn with the darker colors here and of course you could change the color function and draw it in any wild array of colors that you like so does everybody understand or everybody understand what it is we just did here so we drop down another dimension and now we're representing the orbital as a three dimensional object using a two dimensional contour plot all right okay so now the last thing I want to show you with regard to plotting then is that these types of functions look very nice if you make them into density plots let's have a look at what that looks like all right so we can get rid of this contours and change this to density okay so there you have a nice sort of fuzzed up plot that sort of helps you to appreciate the fact that we're plotting a wave amplitude here it's a quantum mechanical object the electron in the 3DZ squared orbital of the hydrogen atom okay so that concludes our plotting lessons all right so now we know how to make all kinds of plots and in the next homework assignment you'll get to practice using these representations of the four dimensional functions okay so now we're going to switch gears now and we're going to start to see a new face of Mathematica that is going to be our introduction to symbolic math okay so actually using Mathematica to do you know mathematics and we'll start out with calculus one dimensional calculus we'll do derivatives and integrals okay so this is useful for many things you may find it to be very helpful in doing your homework or checking your homework sometimes in math classes or P. Kim classes so very very handy okay so to begin here I just want to make sure that we're all on the same page with respect to what is the derivative how's the derivative defined okay so I have a function f equals f of x and now I want to define its first derivative so we'll call it f prime of x actually we could call it y equals f of x and equivalently say dy by dx so anybody remember the definition of the derivative you take it's the local slope right if it's evaluated at a point it's the slope of a curve at that point so we take the value of the function at a particular value x we subtract that from the function evaluated at a little increment away from x we divide by that and we take the limit as the little increment goes to zero. All right so that's our definition of the derivative so now let's see how we can do differentiation in Mathematica all right so the first thing I'll do is I'll generate a function that we will take the derivative of okay so let's say f of x underscore colon equals and it'll be a simple function where we could just you know quickly verify the derivatives in our head so it'll be two x cubed plus eight times x squared and then minus three times x and then plus one okay and I'll enter that all right now there's different ways to ask for the derivative so if it's a function of one variable like this one you can use the prime notation so I can just say give me f prime of x all right and you see you get minus three coming from this term and then you get 16x coming from this term and you get 6x squared coming from this term. Okay you want the dot the second derivative f double prime okay so that's just taking the derivative of the first derivative third derivative f triple prime and then finally if we take the fourth we should get zero and we do okay so that's kind of nice there's an alternative way to do the derivative this is a more generally useful notation and that's by using the d command d standing for derivative and the way that works is you say d capital you specify the function you want to differentiate so f of x and then you say which variable you want to differentiate with respect to all right so this should give the same thing as f prime and it does if you want the second derivative using the d command you say d function and then in curly braces you say x and then the second derivative with respect to x all right so you get the second derivative and you can do the third by putting in three and the fourth by putting in four okay there's yet another way of getting the derivative using the palette and so for that we go down here and you can see that there's this little del button here so the way you use that is you push that button the subscript is the variable you want to differentiate with respect to so x and then the other square there is where you put the thing you want to differentiate so this should give us the first derivative of x I mean f of x and it does okay so three different ways of doing the same thing for simple function of one variable now the next thing I want to tell you about is partial derivative so when we have a function of more than one variable we can take derivatives with respect to each of the variables separately or we can take the derivative first with respect to one variable and then second with respect to another one and the way we do that is through partial derivatives how many people have had experience with partial derivatives most okay so just to make it clear what we're doing here now we're going to suppose that we have a function f of x and y okay and the notation is as follows I could take the derivative partial derivative of f with respect to x and I put a subscript here telling me that while I'm doing that I consider y to be a constant okay and so that would just be f of x plus h comma y minus f of x y divided by h the limit h goes to zero okay so it's just like the one-dimensional version we just treat y as a constant and similarly we could define the partial derivative of f with respect to y holding x constant and in that case we would have x y plus h okay alright and then we could also do second derivatives you can do d squared f by dx squared you could do d squared f by dy squared and you could do mixed ones d squared f dx dy alright so I'm going to show you now how to do those using the d command okay so let's go ahead and generate a function of two variables so we'll say f of x underscore y underscore colon equals so this will be three times x to the fourth minus two times y cubed and then plus x squared times y squared alright now if I want the partial derivative of f with respect to x I'd say d f of x comma y and then I just specify I want x okay so y will be treated as a constant now alright so there you have it does that look right this term gives the 12 x cubed the second term gives us zero because y is treated as a constant and then the third term we get six times x times y squared alright another way to do the same thing is we could use this palette we just say we want the derivative with respect to x and then we can put in f of x and y and you get the same thing okay now suppose you want the derivative with respect to y well you just have to change the x to the y in the d command alright so now you can see the first term gives zero because x is constant the second term gives minus six y squared and then the third term gives two times x squared y which you have here the palette just replace x with y same thing alright now next thing we'll do is we'll take the second partial derivative with respect to x so we can say d f of x comma y comma and then we say x two okay so what is that that's the derivative of this guy with respect to x okay so we get 36 x squared from the first term and 2 y squared from the second term we could do that with the palette by using the neighboring button here so this neighboring button is one that's convenient for second derivatives so we could say x tab x tab f of x comma y and we get the same thing alright what about the mixed partial derivatives so now what I want to do is first take the partial derivative with respect to say x and then take the result of that and differentiate with respect to y so that would be like d squared f by dx dy so we could say d f of x comma y and then we put in the curly brackets x and y whoops what did I do wrong there oh sorry we don't need the curly brackets alright so there's that one what if I reverse the order so I say y comma x I get the same thing and so that's an important rule for these mixed second partial derivatives that if those derivatives both exist then the mixed second partial derivative won't depend on the order of differentiation alright let's see how we do that one with the palette we could just say x tab y and tab f of x comma y same result okay so there you have it some examples of how to do derivatives now what I'd like to do next is use differentiation in Mathematica to do a couple of things relevant to physical chemistry problems okay so I'm going to we'll do let me explain to you what we're going to do here any questions on using the d command or the derivatives pretty straightforward okay so those of you who are in those of you who are in chem 131a now are learning about quantum mechanics and you're learning that variables such as momentum and kinetic energy that are just numbers or functions in classical mechanics classical physics can be represented by what are called operators in quantum mechanics okay so for example the momentum can one of you tell me what's the momentum operator this would be the momentum in the x direction call it px and the little carrot there is meant to indicate that it's an operator okay so this thing by itself doesn't mean anything it operates on a function so for example the wave function okay all right what about the kinetic energy I have this upside down don't I? Yeah it's h bar over i sorry okay oh and by the way for those of you who haven't seen it before h bar is the Planck's constant divided by 2 pi okay so the kinetic energy which maybe we could call say k that's defined as the square of the momentum divided by 2 times the mass of the particle okay and what the square here means is that we first operate on the wave function with the momentum operator and then we do it again okay in this case we can kind of see what's going to happen we're going to get h bar squared the i squared in the denominator is going to give us a minus sign and then we have divided by 2m and then we get the second derivative with respect to x okay so those are differential operators in quantum mechanics corresponding to the momentum in the x direction and the kinetic energy the corresponding kinetic energy all right so what we'll do is we'll evaluate those for our one-dimensional particle in a box which has the wave function psi of x 2 over l to the 1 half sin n pi x over l now what we're doing here is we're just going to apply these two guys to this wave function and those of you who are taking Chem 131a now know that that in itself doesn't produce anything meaningful in order to produce the actual value of these quantities we'd have to do more work but we'll get to that later after we talk a little bit more about once you have probability distributions how you actually get so-called expectation values out but for now we'll just use this as practice for you know doing the differentiation on something that's relevant to physical chemistry all right so what we'll do to begin with is we'll go ahead and oops where did that go type setting we will go ahead and put in a wave function psi make a function of x colon equals 2 over I'll use a little l for the length of the box and then raise that to the one half power and then multiply it by sine oops n times pi times x divided by the length of the box okay and now we'll evaluate the momentum operator acting on the wave function okay so I need to put in h bar over I and there's the h bar right there so I can make it look nice and then I is the capital I and then I say d psi of x with respect to x all right so that gives me the following result now like I say this thing that we just did here is only part of what you would actually be interested in doing if you're wanted to evaluate the value of the momentum but it's just a little exercise of differentiation so that we can see how you know we might use it in a real problem okay what about the kinetic energy all right well for that we need minus h bar squared divided by 2m and I'll put that in parentheses and now we'll multiply it by d bracket psi of x and now we need the second derivative so we say x comma 2 and we probably should put a parentheses in here and I need to make sure that I have a star here okay all right so then now we've seen the result of applying the kinetic energy operator to the wave function for the one dimensional particle in a box all right so one of you in chem 131a if I actually wanted to evaluate the expectation value of the kinetic energy the observable value what would I do next well what I would do next is multiply the complex conjugate of the wave function with the result of applying the kinetic energy operator in this case it would be the same as the actual function because it's not a complex function and then I would integrate over the length of the box okay all right so there's one example now the next thing I want to do is an example from thermodynamics which those of you who are in chem 131 now will see I guess in spring quarter so here's what we're going to do all right so in thermodynamics there are a couple of properties material properties one is called the coefficient of thermal expansion and it's given the symbol alpha so what this is a measure of is how much does the volume change of some substance when I change the temperature and it's defined per unit volume okay so how much does the volume change and it's for constant pressure mean that means dv by dt at constant pressure okay and it's done per unit volume so the actual definition has one over v in front all right so if we have an equation of state like the ideal gas equation for example where we know how the volume depends on the temperature we can evaluate this derivative and have an expression for this quantity all right another material property is called the isothermal compressibility it's given symbol kappa what is compressibility sound like to you because it sounds like something like how much does the volume change when I apply pressure does that seem sensible and isothermal means constant temperature now what do you suppose the sign of this is do things get bigger when you squeeze them no they get smaller so this derivative is in general going to be negative and the quantity itself is defined to be a positive number so it's got a minus sign in front of it and it's also defined per unit volume okay now what we're going to do is we're going to evaluate these for the ideal gas law okay now the details of these are not important to our class this is just a problem where we want to see how to use differentiation to do something relevant to physical chemistry and those of you who are in chem 131 will get to do this later on in the year okay so first thing we'll do is we'll notice that we want to take derivative of volume with respect to both temperature and pressure okay so we're going to define the volume as a function of temperature and pressure so say v is a function of t and p colon equals so what is that going to be for the ideal gas law and whoops little n times r times t divided by p okay and I'm going to start by clearing r because we were using it earlier okay and then we can enter that function all right now we want the coefficient of thermal expansion alpha so what do we need to do take 1 over v times d v of p and t and then t okay so this gives us the expression for the coefficient of thermal expansion whoops I should have said t and p sorry all right so it's nr over pv or in other words it's 1 over t all right has units of Kelvin to the minus 1 now we'll do the isothermal compressibility so that's going to be minus 1 over v times d of v of t and p and now we want the derivative with respect to pressure okay so that comes out to be nrt over p squared v but nrt over v is p so this is actually 1 over p if you wanted to simplify okay all right so there's a couple of examples of differentiation that are relevant to physical chemistry and I think we'll call it a day here any second now next time we'll do another example and then we'll start to talk about the much more challenging problem of doing integration so maybe between now and Thursday you can remind yourself that differentiation is easy, integration is hard and we'll see some examples of that next time they seem like they're you know integration is like anti-differentiation but for some reason that turns out to be a lot harder than differentiation so we'll get a reminder of that next time okay so see you then


I'm Heather and I'm voting yes for marriage equality and I want you to vote with me. What's the difference between two guys getting married, two girls getting married, or a guy and a girl getting married? It makes no difference and how is anyone's life worse because of it, so I'm voting yes.


Okay, thanks again for joining in Let's pray and we'll get started. Shall we? Heavenly Father, we Come before your throne of grace. We humble ourselves before you. You're before your presence And Lord how wonderful and how beautiful are you Lord? How magnificent how holy How lovely are you Jesus Or we thank you for another day another week That you added into our lives.  We thank you for your promise that says you will never leave us nor forsake us So thank you for everything For who you are and what you're doing in our lives in each and every single person's lives and Lord as we continue to read about and study about Your heart for us Lord, I pray that Holy Spirit that you would fill us with your knowledge with your understanding with your wisdom To understand your heart for us Jesus as we study about the subject of healing and deliverance father. I Pray that our heart would be filled with compassion just like your heart was In Jesus name I pray amen Amen, okay Great. I hope you all are doing well We were in the last class be covered a huge portion of chapter 7 in your your hard copies So from page 159 Some of the things that I just want to do a quick recap of everything we've covered in the last class chapter 7 is practical guidelines on ministering healing and One of the things that we highlighted was that you can speak about this same topic Same points and just change the name of the title To practical guidelines to receiving healing. You will have two different summons with the same points, right? So Couple of things few things what we learned was be minister healing through the personal faith in God through the prayer of agreement through the prayer of faith Through a word of command Through the laying on of hands through the announcement of faith through acting in faith Through the gifts of the Holy Spirit through the healing anointing through special anointing through repentance and renunciation of sin Through deliverance through the exercise of faith when celebrating the Lord's table through the use of prayer cloths through other unusual methods And that's where we kind of stopped at but I hope you had a chance to go through the rest of the chapter when you did but before we move on to chapter 8 I just wanted to Talk about a few things in chapter 7 as a conclusion in again and you see that in page 119 in your PDFs and a page 180 in your textbooks 180 in your hard copies I just want to talk very briefly about Getting people to exercise their faith and we'll kind of conclude this chapter, right? Is that okay? Are you all with me? Just give me a yes Okay, a thumbs up or whatever Awesome. Okay, cool. Thank you Right, so getting people to exercise their faith It's very important So a few simple guidelines when encouraging people to step out and exercise their faith Do it by spirit It ensure that the Holy Spirit is prompting you to speak this to them Otherwise bring positive encouragement so that they do what they are comfortable doing while exercising their faith Do it by the spirit Be led by the Holy Spirit that seems to be like the theme that has to be the theme of everything that we do in life But especially in this ministry is just being sensitive to the leading of his spirit Holy Spirit What are you telling us to do? What do you want me to do? Just being surrendered to him Which leads us to the other point that says do not be presumptuous Right, for example, if you're praying for a person, you know person comes and says please pray for my eyes You pray for them and now you don't you don't tell them to take their glasses and okay, okay You don't need this through the glasses off You know, you don't take the place of the doctor right that's acting of that's Just acting very ignorantly, right don't be presumptuous, okay So an example mentioned here is if a person using visual aids such as glasses or contact lens Say they are acting their faith and presumptuously get gets rid of their visual aids There could be serious consequences On the other hand when their eyes are healed Wearing glasses would be very uncomfortable for them That is the right time to take off their visual aids you you know you can ask them so and One of the things that you can always do after praying for them and after asking them to exercise their faith and You know in this context if they just prayed for their eyes instead of Acting ignorantly taking their glasses and throwing it away or whatever You know, you ask them to remove the glasses and see if they can read well like they you know And if they couldn't read well And and then ask them to go back to their you know to their doctor and get their eyes checked and whatnot Right, it's always good to be led by the spirit not to be presumptuous or ignorant or act out of Your arrogance. There's a there's a tinge of arrogance also involved in that Right. Don't let the excitement of the moment cause you to act foolishly Exercise wisdom Right and that will come by being led by the Holy Spirit Do not take the doctor's place. I don't give medical advice. Don't say, okay You need to stop taking your medicines now. You don't have to go to the treatment.  Okay, let them do this based on the consultation with their doctor Okay, so these are very important points for us to keep in mind when we are ministering in healing and deliverance, right? I hope you guys are with me And another thing which we've also spoken about in the previous chapters is to teaching them to maintain their healing Right to You know people need to learn how to meditate in the word of God once they've been prayed on You know, once they've been healed right to meditate on the word of God to build their faith in God to keep their healing and Walk in faith, right? I cannot walk ignorantly after again. We've spoken of so many examples, right? We If you've been healed of diabetes You will do you will take every precaution to walk in a healthy manner and not walk life and do life Ignorantly and and open doors or create circumstances where that That disease can come back Okay And so teaching people to maintain their healing to meditate in God's word to walk in faith to that builds their faith as well Okay So some of the personal preparation to minister healing. This is coming down to us now as leaders Personal preparation and how you can prepare yourself to minister healing It's the foundation the fundamental and the most basic things is growing in the word of God Are you growing in the word of God? Do you love the word of God? Are you steady studying the word of God? Are you meditating on the word of God? Are you just letting his word dwell in your heart meditating your heart? You know grow in your heart, right? So let the word on healing Anointing miracles deliverance authority be established richly in us through Continual meditation someone is a classic example of that, isn't it? Our faith in God must be strong and one of the ways faith is developed is through the word of God So grow in the word ask yourself if you're growing in the word Growing in the annoying thing Okay, so growing the word growing the anointing You know develop deep communion and sensitivity to the Holy Spirit Praying in tongues worshipping him setting aside time To just grow in that intimate Relationship with him is key and that is how you grow in the anointing and you also grow in anointing by Serving under other leaders or other ministers of God Who are in this ministry? Right, which is very important as well. So desire for more of his presence more of his power And pay the price any price that needs to be paid to grow in the anointing Okay and because that The same anointing that all these great generals of God has functioned under you know from Charles Spurgeon to a John G lake To anybody that you want to mention Catherine Coleman or Benny Hinn etc etc whoever you want to mention Who's had a very successful healing ministry? It it's the same Jesus who anoints them And it's the same Jesus who wants to anoint us and fill us Right and the again it all comes down to your question your your side of the equation is how far Or how much of the price are you willing to pay? Right. Are you willing to go after him to seek him more? Are you so growing in the word growing in the anointing? Growing in intimacy through obedience prayer worship and fasting maintaining purity of heart We must maintain a pure heart. We must guard our hearts from wrong motivations from competition jealousy pride and self This is one of the reasons why we do during the orientation of pc We do this we cover a pc publication laying the axe to the root If you remember, I think we did this for you guys also Right laying the axe to the root and there we cover all of these things Right guard your heart from jealousy of all from pride.  So I do everything in your You know in with your within your power to Protect your heart to guard your heart To constantly keeping the prayer saying search me and know me see if there is any wicked ways in me Allowing God to look into your heart and say lord Let my heart be steadfast Let my heart be steadfast. Let my heart be steadfast.  Let no jealousy or pride enter me at any point in time Right, because this is very clearly the downfall of It can be the downfall and I think I've I've I've been in ministry as a christian and in ministry long enough to see that That how these two things have destroyed people that is jealousy and pride Um I hope you understand what I'm talking about correct, uh, right If it just absolutely ruin your life So do everything in your mind to guard your heart to protect your heart. You guys with me Yeah, um, so grow in word grow an annoying thing grow in intimacy through obedience prayer worship and fasting A maintain purity of heart Now grow in faith through stepping out Grow in faith through stepping out Time and time again. We've spelt faith as risk. Isn't it? R. I. S. K. So you take that step of risk And you know, and and that's how you will grow in faith Take that step of faith and pray for the individual that you see that needs to be prayed for Don't be afraid Ask the holy spirit to guide you to give you the spirit of boldness because he has given us the spirit of boldness and courage Right and finally always giving god all the glory Always always always always Give god all the glory Right, um, because with me this is these are all just fundamental Basic points for any christian any believer to grow in Right, you grow in the word grow an anointing intimacy to obedience prayer worship and fasting Maintaining purity of heart Growing in faith through stepping out and always giving god all the glory Right, and if all this is set in place, you're on the way to a very successful ministry Right you guys with me alive Okay Okay, now let's go into the next Chapter Chapter 8 A simple model for ministering healing Right a simple model for ministering Healing One of the key points in this course is it's one of the many is that It's not only the pastors or the evangelists or teachers who can minister in healing and deliverance, but The point is to encourage every believer to step out and And minister healing and deliverance Okay, and so out of that In the last chapter we learned about some of the guidelines to ministering healing and deliverance and this chapter We'll we look at a model Okay, so model for ministering healing. So what is a When you when you say, okay, this is a model to minister healing or this is a model to do something Why is it important you in do you think it's important to follow a model Or a blueprint You think it's important to have some kind of a blueprint before we Start building something Yes, no maybe so You know this chapter is built upon the The teaching by john whimper This is called a five step model Which is presented by john whimper now john whimper is the founder of vineyard ministries John whimper used to work for a corporate company for the longest time and one day he gets frustrated about okay Okay, you know about his life saying what am I doing for his kingdom and whatnot he And so he starts this ministry which which is now popularly known as vineyard Most of you would have heard it and it was a beautiful moment in the 80s in the 90s A lot of churches have been planted worldwide And so many songs have been birthed out of this movement Which was started by john whimper The founder of vineyard churches okay, so we we learn of You know a five step model to how to minister healing But what I want us to keep in mind is that this is not the only way to minister healing Okay, but it is a simple model that has been taught and it's been effective In a bearing powerful fruit in So many people's lives and so that's what we will be looking at today in this chapter Okay, another point that I want to reiterate Is that as we go through these different steps of this as we go through this model Remember that the healing is in the person of Jesus Christ Healing is in this presence and not in the process Right. So having said that let's look at the first step in this model of ministering healing Uh The first thing is what we first step is what we called as the interview Right. So a person comes to uh, you know for prayer requests for prayer And you begin by asking okay, what would you like me to pray for? Okay, uh, where does it hurt? Etc. Right. What can I pray for? So you begin with that question okay now Please note that you may we may not have you know the time to ask all these questions You know all the time People will sometimes you have 50 people 100 people coming to just pray And sometimes you may have the chance or the opportunity to ask them And there will be times where you will not have the time Or the chance to ask them. So it's okay. Remember. This is just a model. Okay It's a good place to start. It's a good reference point for us to learn to minister healing and deliverance And so ask them. Okay. Uh, where does it hurt or what would you like me to pray for? Um, you know, some of the questions that we can ask is what is your name? Uh, you know, what would you like to pray for?  Do you know what the cause is? Have you seen a doctor? What the what does the doctor say? about this Do you remember what was happening in your life and this condition started? Did anything traumatic happen to you about the time your condition began or within a few months prior to starting? so You see what I mean by that you will not always have the time to ask all these questions Right. Uh, so it's okay if you don't get to ask all these questions It's just a reference point and see what kind of question is appropriate at that point of time For you to take that step. Okay. Most of the time at least in from my experience. It's been What is your name? That is just to become get more personal and to pray for them specifically if you if you don't have the time to get What their prayer request is and whatnot if there if there's a lot of crowd and whatnot What I would suggest or encourage you to do is to at least get their name And so you can pray for them by their name Okay, so you ask for their name and then you ask them for their condition You know, what can I pray for? Uh, is there anything specific that I can pray for? How did it happen? What did the doctor say about it? Etc etc That is the first step right because you're getting specific about it. You're not just doing a random prayer You need to know. Okay. It's the pain in the right wrist or the left wrist. It's a certain x-ray You know, that says a certain fracture And what must you as you get more specific you get to speak to that condition directly Right. You say for example, okay, it's the left wrist That's broken And if it's a certain and if the person even says that this is certain bone because every bone has its own name But it's okay. And you speak to that particular bone to that condition to that fracture You know, and do you declare the name of Jesus over that? It's all about getting specific Isn't it? So that's what the step is all about. So once you finish the step one, you kind of begin the diagnosis You can ask begin to ask yourself and them Why do they have this condition? Right. So this step is about identifying the root of the person's problem There's again, if possible And now this step is not always necessary Okay, this step is not always necessary, but it's helpful In as we minister healing and deliverance to this person. Okay, so Now in the first step, you're in you're asking all these questions to the individual say, okay, what's your name? What's the condition? What can I pray for and whatnot? As you are listening to this person, you must also listen to what the Holy Spirit is saying Right, your heart is in line as you're listening to this person. And you know, it's uh Yeah, it's like multitasking. I guess okay, so you're listening to this person intently And you're also asking the Holy Spirit, Holy Spirit Uh, help me out here. What do you have to speak to this person? What do you have to say about this person? How do you want me to minister to this person? Right and so at that point of time as the person has finished sharing the Holy Spirit may give you a word of knowledge Of a vision or a picture or something some insight for you to in helping you to minister to that individual Right, so this step again is called as the diagnosis as to why they have this condition It's not always necessary. But then If you go through this step, there may be several reasons as to why you may think that this individual Has a certain condition, right? It could be several right. It could be a natural cause A disease or an accident or it could be a sin committed by them or to them Uh, right emotional hurts causing physical or other pain relationship problems a lack of forgiveness or or supernatural And and maybe demonic right for example, let's say a person Comes and shares You know and and they say that they haven't been able to forgive a certain individual because they've hurt them You you immediately know what the issue is it's unforgiveness that has led to bitterness and you kind of ask them, okay How long ago was this, you know, this person did something 10 years ago And this person has been dwelling on it for 20, you know, 10 years You know, they've been holding that offense in their heart and that's led to That offense has led to unforgiveness and that unforgiveness has led to bitterness and bitterness has opened the door for The the demonic to you know, take a foothold in their lives and so you immediately know What what the condition is and what has caused the condition? and now you know To what you have to speak to and declare to Are you guys with me? Are you guys following what you know, uh, the importance of this step, right? I hope you are with me Right. Um, so again, uh To reiterate as you're listening to the person it is extremely important You're not just praying, you know for this person. Yeah, it's like See as christians as ministers as leaders We get used to praying to a lot of people Right, uh, maybe at the beginning of the service or the end of the service people come to say is like pastor Can you pray for me and what not and and it is it is very easy for us to treat That individual like, okay, let me just pray and move on in life because i'm very tired It's very easy, but um, so you know, there's one thing I learned I used to work in a call center Between 2005 to 2009 It's quite some time ago So and I would take approximately A day On an average I would get a hundred calls. So that's hundred different customers Okay, um, so one thing what I learned is they would say Look guys, you know It's true that you might be getting a hundred calls a day. That means it's a hundred different customers Uh, and for me it's a hundred different customers, but for them It's their first call to you Are you with me? So they're not going to understand that you they are they are the 60th person to call you They are the 99th person to call you So you don't expect them to understand that you are tired and what not you treat them as As if they are your first customer Okay, this is just a little corporate insight Uh, and so similarly for us as leaders as christian leaders as pastors It's very easy for us to get into that zone.   Okay, you remember what we've learned It's not about the method or the process. It's in the person of jesus and its presence Okay, but then you choose a method to to minister some of the common ways to You know become the common methods is laying on of hands anointing with oil Petition simply inviting the holy spirit asked for healing Intercessory prayer The command of faith pronouncement of faith Binding and rebuking demonic powers for giving and renouncing past hurts and wounds Okay Couple of things to watch out for one of the common ways as mentioned is laying down laying on of hands Oh What what I'd like to do is Be it The same sex person or the opposite sex male or female. I'd like to get the permission of the person I asked them is okay Uh, is it okay if I lay my hands on your head? Is it okay if I if I hold your hands? um and and I think it's It's a it's a good thing to do right because you don't know Uh, how an individual might feel someone some might feel okay and comfortable with you laying your hands on them And another individual might not it doesn't matter their gender Or it could be male or female. It doesn't matter But as soon as you ask their permission and I think it allows it Uh, it's almost like they are a lot. They're okay. They're letting yourself they're letting, you know, you're in To say, okay. Yes, you can come and lay your hands on me Right, or you could if they are not Uh You know, you could ask another person to lay their hands on that person the way it's hurting We could ask the person to do that for themselves. Okay, so laying on of hands anointing with oil Um petition intercessory prayer um Forgiving and renouncing past hurts and wounds That that is, you know, lead the person in a prayer to forgive those who have wrong or uh Sorry, I thought something was wrong there You lead the person in a prayer to forgive those who have who may have wronged Or depend of doing wrong to others Uh, right again, these are all uh, some of the methods ways in how you can minister um To to the person that you are ministering to okay. Um, there is an example that is mentioned in your notes. Let's take a look at it Um For example, here is a ministry that is a combination of several things. Let us say a person named john Has several problems in their lower back due to an injury Here is one way to minister. Okay.  I command healing to john's back. I command healing to the vertebrae Discs and nerves and command these to go into their proper place Come holy spirit release your healing virtue on john's back and make him completely well in jesus name Okay, this is again one of the ways uh to minister To a person one of the methods that you can use there's multiple methods that's involved there Here Okay, any thoughts any questions guys so far? Okay. All right Let's move on to the next section. Um The ministry ministering and watching what god is doing Okay, uh, the ministry itself as you are praying now Uh, you also watch what god is doing right? So while we are ministering, uh, We would normally keep our eyes open to see what god is doing Don't have to but you can keep your eyes closed as well Uh, you know, but you know as we as we see slight improvements We are we are being encouraged and we are encouraging the person to act in faith as well Right and so you ask the person if they feel anything or do they feel any difference? You know and most of the time someone would say You know, they would say okay. I feel like a heat going through or like a wind that's blowing etc etc and then, you know Uh, if you try one kind of prayer or command and get results, but not complete healing Uh, continue to explain to the person that god wants to God wants them completely well Right and so you you continue to pray for them saying, okay, you know, I I could not stretch my hands fully For example, if you've been playing praying for their uh for their elbow or whatnot They're saying I could not stretch it out fully, but I'm able to stretch out so much and my pain has reduced Uh, you continue to pray and say, okay. Can I continue to pray saying god wants to heal you completely and hold Right, so you continue to pray and whatnot so And in this process another important question to ask is uh, when do we stop? Right, so you okay now you've prayed you've seen partial improvement partial healing That this person has received When do you stop a couple of pointers for us to remember is you can stop when the person is completely healed That's one thing Right, uh, and or when person says when the person wants you to stop. Okay, pass a thing. It's enough. It's okay Um, you don't say no. No, I will pray for you No matter what uh, they will not come back to your church Uh, right, so when the person wants you to stop respect that honor that When the holy spirit tells you to stop saying hey, that's enough be sensitive and just stop Uh, you're not given any other way to pray or you're not gaining any ground, you know, if you see, okay Uh, okay, there's you've prayed the person has not told you anything What you can do is okay this way what I will say is uh Um Not sure if this is right about the common sense. Okay, let's be okay. You know, you've pushed enough You've tried enough, but you say, okay, uh, you know, you can go back home continue to pray and we will continue to pray for you and And you know, you encourage the person and say a god will come to you god will heal you completely Okay, so those are the few pointers for us to remember as we are ministering Healing and deliverance of the key important points is to make it personal You know diagnose what they're going through And then you minister to them and you choose a method that you want to minister in And and be sensitive to when you have to stop Okay, um, and finally the post ministry suggestions What should they do to keep their healing? Right, uh, what should they do to keep their healing? Um, so if the opportunity arises speak to the person about their personal salvation if they are not yet saved Right, so if they are not yet saved speak to the person about the personal salvation. So uh an unbeliever a non-believer comes and Pray and asks for prayer once you prayed for them and you present the gospel to them Right you and say, uh, you know This is available the gift of eternal life is available through Jesus Christ. Are you willing? To accept So you're presenting the gospel, right? Uh, you talk to them about their personal salvation and And then you also continue to tell them say, you know, you talk about what john chapter 5 verse 14 says Uh, you know after jesus heals the cripple man. He says sin no more less the worst thing come up on you Right, so you encourage them to spend time with god Uh to stay involved with the church if they are not connected to a church You encourage them to get connected or help them get connected to one of the local churches that you might know of In the vicinity I'll get their number their contact details and keeping in touch with them making sure that they are plugged into one of the churches Is is an important method post ministry right, um What if they are not healed This is again a question that we've addressed in the previous chapters, but Reassure them that god loves them Right encourage them to keep on in faith and continue to pray persevere in faith Right, uh, one of the things that we should not do or avoid at all cost is to accuse the person uh Which you are not healed because of Generational curse or some hidden sin or you are not cause you of little faith. You lack faith uh, you know We will never take the place of accusation or accuse the person saying you are not being you are not healed because of this This this this uh, we do not say that at all. We encourage the person saying what loves you It is his nature and his desire to see you made whole Right, uh, and so we are only his instruments if the healing does not happen Uh, we just need to press into him and seek him more And um, so these are the five step model To a minister healing Right. So what are they first thing is the interview You ask them, where does it hurt? What would you like me to pray for? Second is the diagnosis Right, why do they have this condition the root cause or root causes? Uh, and you the method of selection, right? You choose which method that you want to Pray or your minister, right? The ministry the ministering you watch them as you're ministering as you are praying for them You see what is happening. You see what god is doing um, okay, and then post ministry suggestions is What should they do to keep their healing and the importance of getting connected to a church and whatnot All right, guys. Are you all with me? Do you have any questions or thoughts that you want to ask or share? All right, then, uh, there are no questions. We'll stop our session. Let me just stop recording this session


Hello, my name is Belém Tamayo and I'm from Mexico. Today I'm going to tell you a little bit of my experience studying abroad in the Netherlands. And when I started looking for an exchange program or to continue my studies out of Mexico, I really did not know what I was looking for, what studies I was interested on. I just wanted to live in the Netherlands because I love the country. So I started looking for different institutions, different schools. And I was really surprised with Saxon because they really had everything explained on their brochures. Their facilities were in the city center, very accessible for me to just walk in and ask for information. Everybody was so friendly. And when I knew that I wanted to study in Saxon, I still didn't know what to study. So they gave me all this information. They sent it to my home where I was staying in the Netherlands. And I was looking at all these programs and it kind of fit every program fits a personality and interest. So I decided to study international business. And it was a perfect fit for me because it was all the skills that I wanted to learn, but I did not have. So when I decided to study international business now it was all the paperwork. I had to come back to Mexico and do all my visas and get all my certificates in order. So I thought it would be a lot of work. But the personnel in Saxon helped me a lot. They really guide me step by step to know what to do. And every time I had like a bump and a rock in the way, they would help me. They would guide me. They were very friendly. And thanks to them, it was so easy to do all this paperwork. Once I came back from Mexico to the Netherlands, ready to start, the program was beyond of what I expected. I really wanted this college experience with all the friends, with all the teachers and everything. It was so cool to be in Saxon studying. And it was easy to get carried away by all the events and all the parties. But I remember Monique telling me, this is just so easy for you if you come to school and assist to all your classes. So I remember that really in my brain. And I thought, well, although these parties are cool, I will come to school every day. So I I didn't miss a day at school. And it really made a difference. So that's my tip for you. If you come to study at Saxon, enjoy the Netherlands, enjoy the countries around the Netherlands, enjoy the parties that come to school and be there. Participate, listen, make the best out of it. Me as being from Mexico, I knew I had only one chance to succeed. And I did. I graduated the first year with my Papadose. And the last I finished my studies with the four years that are mandatory. And everything was on time. It was a great experience. I had many internships. Now I have a great job in a US company. And now I'm back to the North America continent. And I'm very happy I can travel all over the world. And Saxon changed my life. The experience abroad and the friendly people I make friends forever and my network. Now it's huge. Thanks to this experience. I recommend it. And if you do it, do it with all your heart and all your passion. And you can gain the most out of it.


It's no secret that Joe Biden is out of touch. I think that even his own supporters know that he's out of touch But they're still supporting him regardless because they think that he's more electable Against Donald Trump, which is laughable But I mean it's no secret that he's not progressive right to put it charitably But I think that a lot of us underestimate how out of touch he really is like he made a comment about marijuana legalization Not in 1999 not in 2010 or 2014, but in 2019 That sounds like something a politician from back then would have said So this is what he had to say about the legalization of marijuana on a federal level According to the Hills Owen Doherty speaking at a town hall in Las Vegas on Saturday The 2020 Democratic presidential candidate said whether the US should legalize cannabis on a federal level Is still up for debate as far as he's concerned The truth of the matter is there's not nearly been enough evidence that has been acquired as to whether or not it is a gateway drug Biden said according to business insider. It's a debate and I want a lot more before I legalize it nationally I want to make sure we know a lot more about the science behind it Biden as he asked throughout his time on the campaign trail said he supports medical marijuana and insisted Possession of the substance should not be a crime But he also said Saturday that he thinks the decision to legalize marijuana should be left up to individual states again I want to remind you he said this Recently like this sounds like a quote from a Democrat or Republican like half a decade ago This is just downright embarrassing to still suggest that Cannabis is a gateway drug at this point with the amount of evidence we have I Don't think it's unkind for me to call you an idiot. I think it's just accurate.  We still keep that legal. I Mean how long is it going to take until people realize that prohibition does not work prohibition never works That's why we made alcohol legal It's why marijuana legalization in the states that it has Happened in has been incredibly successful and being from a state that has legal weed. I can assure you We're not going, you know out of our way to acquire meth now We're not graduating on to harder drugs. Nobody's doing that. In fact in I believe Colorado Marijuana use among young people has actually decreased So there's been nothing but positive effects and on top of that we're raising tax revenue that we are funneling to schools and local projects But yet Joe Biden says, you know what? We'll just leave that up to the states Okay Well, doesn't it not make sense that we're still locking people in jail in some states for something that is harmless in My state I can walk into a store and legally purchase as much pot as I want But in other states if you have marijuana on you you could go to jail That doesn't make sense and there are going to be some states who are never going to legalize it more Conservative Republican run states in the South who will never legalize marijuana and this is a civil liberties issue So why should people in the South never have what we have here in the Pacific Northwest? In fact, the whole West Coast has legal weed now. So when you say this is a states rights issue, this is you Pivoting this is you sitting on the fence because you don't actually want to take a real stand saying that you support medical marijuana That's not bold Republican support medical marijuana. That's not a bold stance at all decriminalization is not bold We need to talk about seriously Legalizing marijuana in all 50 states and the fact that you're not going to do that as president Shows that you're a joke. You're offering people nothing. You are offering voters nothing to be excited about I mean, this is an issue that would easily get at least some young people excited to vote for you I still wouldn't be excited to vote for you But if you were pushing this I'd say, okay, well, it makes sense because this is an issue that has bipartisan support I mean, you're gonna get the progressives as well as the libertarians on board. Why not opt for legalization?  He's a hack. This states rights issue is incredibly, you know annoying I think that some issues can be states rights issues. That's fine But on issues like this where it's incredibly popular The Democratic Party and Joe Biden would be absolutely morons to not jump on board with an issue that would make them so popular Who's against weed legalization in 2019? Support for this will only increase in 2020 so you can actually pound Trump for that Take away some libertarian votes in the event you're the nominee, which I hope you're not and say look Donald Trump isn't for freedom Donald Trump doesn't even want legalized marijuana federally What a joke.   It's the wrong answer. It's always scapegoating immigrants But they're proposing answers that speak to people that prey on their desperation and exploited So Democrats who are neoliberal who aren't actually going to fundamentally change the system They're letting you know that they're not serious about taking on these right wing demagogues and fascism and in a way They inadvertently enable it and when we're talking about true systemic change, we can't have true change change We can't have real criminal justice reform if we don't legalize marijuana and I'm not talking about decriminalization I'm talking about legalizing it and allowing people who have been hurt by it the most Who've communities who have been hit the hardest black communities to really have dibs at this new business here Because you know legal weed is going to be a very very large industry. It's already a multi-billion dollar industry So for you to just not get on board and fear monger about it being a gateway drug in 2019 It just shows to me that Joe Biden if you were to go up against Donald Trump It's gonna be a bloodbath and not in his favor.


Let us look at some example services which service overlay networks may offer. For that we have to convince ourselves about the need which emerges and justifies the deployment of SONs and then we look at the services themselves. So the first and most important thing is that although we do have the service stratum and the transport stratum and end user applications can directly engage with the NGN service stratum and use the entire NGN infrastructure. It is very much possible. But at the same time the kind of evolution and the kind of continuous improvement which is taking place in the service sector means that the services are going to emerge at a very fast rate. So it means that there should be a mechanism that allows the NGN to be used by the service providers these services and these services are provisioned to the end users in the most seamless manner. So that is actually primary motive for the adoption of SONs. We have certain examples that we are going to look at including the classical example for NGN that is IP based TV that is stored or streaming TV service. Then we have certain community based services. We have the virtualization of home network and cloud computing. So all these are very interesting and fascinating ideas. Let's start with IP TV first. IP TV is one of the most quoted and one of the most important concerns for the adoption of NGN and for benchmarking the performance of NGNs. So IP TV services are offered in a variety of ways. For instance it could be NGN or non-NGN based IP TV service provisioning. Within NGN it could again be IP multimedia subsystem based IP TV service provisioning or non-IMS based. So we can say that there are a variety of alternatives, options, choices which could include different kinds of IP TV content. It is coming from the non-Telco or non-NGN provider network for instance a third party. In that case it becomes important to come up with a SON kind of mechanism for IP TV service provisioning. There could be for instance a customer oriented IP TV that is an IP television function which is provided by a certain community as a podcast so they can offer it as a SON based service. If IP TV has to be provided then some of the most important considerations that IP TV has to expect from SON is the session control because in multimedia traffic managing a session is quite of a concern especially once a device like a handheld PD or a smartphone is on the move, security has to be ensured and then the service has to be provided amongst a certain community. It could be a closed user group for instance a multicast group of some specific content interested people for instance students or a business community or a professors. Then SON in turn expects the service control functions to be invoked so that a user actually can interact with the application and in turn with SON services for personalization and for other kinds of modification to the choices. Let's look at certain community services. These community services could be custom services which have a particular audience. It is basically a data service which is offered to a group of people who form a logical group so they actually come up with a head or a master who decides what is going to be the QS requirement, what is going to be the security requirement and all these things have to be defined for a certain session. So these users could be non-contiguous, non-neighbor network-based individuals who are coming from home networks or customer premises networks for instance head offices or the branch offices of an organization or even could be coming from the public access networks like Wi-Fi hotspots, Bluetooth hotspots or even LTE-based networks. So it means that all these different users have to be provided IPTV service or any other community service in a very seamless manner. So this is exactly where SONs become relevant. Then we have virtual home network. So let's look at what is a home network.  Even you can form your own private network where you can interact or play games with your family on wireless LAN. So it is a typical home network. But you can create something similar to a home network as a virtual network by connecting again the physically non-contiguous devices into a logical interconnect. So these could be from altogether different locations. So once a home network is formed virtually then the participants or the users of that particular home network can share data services and common interests. The last one is again very hot and trendy these days. It has become more of a buzzword. But the underlying concept is very much related to SONs that is cloud computing. Cloud computing is essentially a distributed computing environment where basic computing functionalities for instance storage, processing, different applications like office applications are offered to a number of users in fact a very large number of end users who are connecting to the NGN through their own desktops, laptops, smart phones, etc. For as long as they have IP connectivity and as long as they are connected to NGN they are very much in a position to avail this cloud computing service on the basis of SON connectivity. Now these services are offered like typical client server architecture like web server where a client browser requests content from the web server. The beauty of us having service overlay network between the user applications asking any of these cloud computing service and the underlying NGN architecture is that SON provides complete transparency in fact complete independence from the underlying infrastructure so which particular software is providing the service where is the hardware situated who exactly is providing the service the network administrator or the owner of that particular service provider it is the beauty and essentially it is not much different from how typical web based services and applications work so from SON if such cloud computing services have to be offered to users what are the expectations. The expectations are that some kind of contract should take place like service level agreement then security configurations have to be reconciled and agreed to then services have to be provisioned if certain applications have to integrate certain services like infrastructure as a service software as a service or any other kind of service like platform as a service then all these have to be integrated and over time depending upon the user requirements and user subscription these have to be adopted and adopted so this is essentially what cloud computing is as a SON service based application.