My wife and I have always tried to stay connected to what our children were doing in school. When you maintain that communication with your children, you're going to hear the education that they're receiving. And I've really taken that to heart. I think that if I want to know my child, I want to know his world. While the best way to get plugged into Cal as a parent is to participate in Cal Parents. Now that I've been through it, I wanted to let other mothers and fathers know that this is a great place for your student. One of the things we love to do is to meet new parents at Move-in Day, where we also, of course, meet our new students.  We also see the anxiety and the nervousness about letting your children go, but they're in great hands. We know you want to stay connected with this campus when you send your children here, whether they're undergraduates or graduate students. The Cal Parents program provides all kinds of opportunities for you to do that. For you to connect with the academic programs here as well as the extraordinary range of opportunities that exist, not just for your students, but for yourselves on this magnificent campus. Cal is unique because it has everything. There are lots of schools that are really good at engineering or really good at the arts. But Cal is a place where no matter what it is you're interested in, somebody here is doing it really well. Everything is so different and so good and that's what benefits us is that we draw from this diverse group here. As we grow we continue to build off that and that's what makes it great here. The theme of excellence I think definitely does encompass everything. It's really funny because the thing that people always say is where you are from you were the best in your school. And so UC Berkeley is kind of like that center, that epicenter of all these excellent people coming together. And so you kind of feed off of that, you get the best students, you get the best professors. You know, this is really one of the greatest universities, not just in California, not just in the United States, but in the entire world. It routinely gets rankings in the top five for virtually every field. When we invite your children to come here for their education, they can participate in really some of the most cutting edge research and some of the most extraordinary educational opportunities available anywhere in the world. I'm a professor in residence in Christian Hall, which is in unit one. The faculty in residence program is a program that brings faculty to live in residence halls with undergraduate students. We serve as mentors, guides and friends. The professors are busy and have research, but if you sit down with them and you go to their office hours, they really want to help people learn and they want to make your education as meaningful as possible. So every experience I've had with going to office hours and meeting up with teachers has been beyond what I expected. The faculty at Berkeley are phenomenal, right? So even in a large lecture course, students are getting the cutting edge of the field. I think it's really up to the student to search out all the resources that Cal has to offer. It's very easy to make Cal kind of smaller. It's that thing I'm sure you've heard it so many times. You know, you can make a big school smaller, but you can't make a small school bigger. I was an undergraduate here. I was taking courses from faculty members who had written the books, right, who had written the textbooks. And what that meant for me was that I started to think, wow, so creating theory is what people do. And so it kind of in some ways humanizes the research process and the theory-building process that allows you to think, well, maybe I could create theory too. Cal Parents is fabulous and we have, I'm proud to be a part of it because we funded so many amazing things, like freshman seminars, which are this marvelous opportunity. Freshman seminars are 15 students getting together with a faculty member once a week to work on something interesting. So I'm teaching a freshman seminar this semester on the physics and technology of siege engines, things like catapults and trebuchets. Put some minions together to see if you can build those triangles. And there are clamps in there to clamp them before you screw them and glue. I love teaching at Cal. I love the undergrads. I love the graduate students. I love everything about it.  They're a bunch of people working together to improve their understanding. You know, we're not going to win a Nobel Prize for freshman seminar work, but we are going to learn something as individuals. We're going to learn something as a team. And we're going to teach students that curiosity is a big part of learning. Well, I've been involved with Cal Parents since the year 2000. I was in Sprawl Hall walking around and I saw this door and said, Cal Parents. So I thought, I'm just going to walk in here. So the Cal Parents program is a great way for parents to stay connected when their child joins the university. Cal Parents is a program at Berkeley designed to support families and have families become a part of the Cal experience. There's resources at the Cal Parents website. There's a Facebook site. There's newsletters home. There's volunteering opportunities that can bring you to campus, but you also can volunteer in efforts that happen in Southern California and you can meet other parents that way. I love the Discover Cal programs because in Southern California it connects me and I feel like I can hear that professor talking about Egypt or talking about this particular environmental issue that's current in the news today and it's not very far. I think what's nice about Cal Parents is that we can respond immediately to issues that are hot on the table and we're very connected to what's going on on campus. I'm more engaged on the fundraising side. I think it's very, very important for the parents to recognize that Cal today needs the kind of financial support that the private schools have in order to stay competitive. I felt like I have to fight for what is so wonderful. I don't want it to go away. I've had two kids attend Berkeley. It's been a wonderful experience for both of them. I am a new Cal parent. My daughter started here this spring and she is having a blast. I was the only one that I could say it. It's a marvelous experience. A sometimes an overwhelming experience. Sometimes an experience that makes a dad really, really nervous.  My biggest piece of advice is to let your kids lead the process and trust that you've done a fabulous job and they're ready. Advice parent to parent having had one daughter graduate and another one about to relax. It's an amazing world. Your kids are going to go through incredible experiences that you can't conceive of. Let them do it. It's going to be okay.


Welcome to Every Way Woman. The other day, I did an exam for myself when I felt the lump, and I still haven't gone to the doctor because I'm making those excuses. It wasn't pretty for me to be in my 30s to find out that I have menopause. I thought about the pill, the IUD, the Nuvo ring. In my own mind, I never thought about condoms as birth control for women. Sex. That's cardio. You'll get a partner to last 30 minutes. I'm going to talk about menopause because, frankly, it's something that most people aren't talking about. My hormones are both raging, and I just felt completely out of balance. But now that I've gone to menopause, finally, my body's at peace. I was younger and still to this day. I try and just, you know, power through. And I think women do that a lot rather than, you know, we listen to our bodies, but we're trained to tolerate so much.  I really feel that I'm the patient. So for the people in my generation who, one day, is A, and the next day you don't know your parent, what can you do to help us with the stressful moments? What could I have done to be prepared? Because I'm so not prepared, and I'm really stressed. There are some major changes happening in the talk show world. If you were as the audience, the real women and men out there are trusting us.  Used to be this very deformed look of a picture is called a radical mastectomy. Take the whole breast, even the muscle, sometimes even the ribs, 50 years ago. If they're in their young, early 20s, likely even after chemotherapy, their fertility will be okay, but you can never guarantee. We're trying to give or create segments where people know what questions to ask. What's your question? Why isn't there more information on the severe side effects of cancer treatment? Many of us in the medical oncology community know that in the last 15 years, we've seen a big breakthrough in nausea, very potent nausea medicines. Is there a better time for me to check my breasts? Good point. Men's trading women should do it five to 10 days after the onset of their period. We all know once we hit 20, we should start doing breast exams. I noticed a change in my breast shape. I felt a lump in my left breast. And I found a lump. I found the lump in my breast.  To be 100% honest, initially I denied it. If you were to lose some of the skin along that decision line, usually what we do is we remove that skin and just close again. The same way we removed the nipple in the beginning. I found our segments really useful for me, being single, somebody that never really looked into going to the doctor when I was younger. For more information, please visit our website, EveryWayWomen.com. I thought you were an every-way woman.


In this lecture and the next lecture, we are going to discuss how to solve first order partial differential equations in the sense that how to obtain general solutions. So, in today's lecture, we will discuss about general solutions to linear and semi-linear equations because it is easier and we see how to extend these ideas to the case of quasi-linear equation in the next lecture. So, the outline of today's lecture is first we discuss a useful idea in finding general solutions and then we move on to linear equations with constant coefficients because that is a simplest case and from there we get an idea and try to solve linear equations with variable coefficients. Semi-linear equations follows very similarly to linear equations because the part where the first order partial derivatives appear in both linear and semi-linear equation they look alike. So, useful idea in finding general solutions. So, general solutions to linear and semi-linear equations can be found using very simple ideas. We will see in the next lecture how to generalize or extend these ideas to the case of quasi-linear equations. The method resulting out of these ideas is a famous Lagrange's method for finding general solutions of quasi-linear equations. So, let us discuss a linear and semi-linear equations now and what is the key idea behind this method. So, first of all observe that the partial differential equation is linear in first order derivatives. The terms involving first order derivatives look like a directional derivative. We will see more on this in the next slides. Now, what happens is change of independent variables will then convert our PDE into an ODE and we are experts in solving ODE's. That is why ODE's are easier to solve. So, that is why this strategy we will follow. Recall linear equation of first order is of this form AXYUX plus BXYUY equal to CXYU plus DXY. This we denote by L and the coefficients A, B, C, D are C1 functions of omega 2. Omega 2 is a subset of R2. Of course, there is another way to think of this as a special case of quasi-linear equations in which case A of XYZ will appear but A of XYZ is independent of Z. So, asking it that A of XYZ is C1 of omega 3 is same as asking A of XYZ is C1 of omega 2 because it does not depend on Z. And we do not want both these coefficients of the partial derivatives to vanish at the same time in the sense at the same point in omega 2. So, at every point in omega 2 at least one of them should be non-zero. And then semi-linear equation of first order looks like this AXYUX plus BXYUY the left-hand side is exactly same as that of L whereas the right-hand side C of XYU that is a semi-linear equation. And assumptions natural are A, B are C1 of omega 2 and C is C1 of omega 3. Of course, omega D are subsets of Rd equal to 1 3 omega 2 is a projection of omega 3 to the XY plane and A square plus B square is not equal to 0 on the domain omega 2. Let us see an observation that first order partial derivatives appear in the same way for both L and S we have already observed this namely this is the part AXYUX plus BXYUY this is the left-hand side in both L and SL. If either A or B is a 0 function what does that mean imagine A is 0 then this above expression is simply BXYUY and the equation would look like BXYUY equal to CXYU plus D in the case of L and BXYUY equal to C of XYU in the case of SL. That means there is no derivative with respect to X will appear if A is 0 in other words it is a ODE it reduces to ODE. Therefore, solving L and SL in such a case is same as solving ODE it is no different from solving ODE. Now we ask a question do not we like if it is true that either A or B is 0 function in every same linear equation? Answer is yes of course we like it but we know that we cannot expect that but we can make it happen. We can make it happen after a change of variables we will we are going to do that now. First let us understand the simplest case it is a linear equation with a constant coefficients. So, let us look at this equation AUX plus BUI equal to 0 coefficients are constants so A and B are real numbers at least one of them is non-zero real number. If one of them is 0 it is a ODE so we do not want to discuss so you can as well assume both A, B are non-zero of course it is not needed for the purposes of our lecture but you can imagine that both are non-zero numbers that is when it is not clear what you want to what you can do immediately. If any one of them is 0 it was ODE you have already solved. So, we place this assumption that one of these A, B must be non-zero real number. Let us look at an example of course in this example I made it B equal to 0 and A equal to 1 this is just an example this will guide us in further proceedings. So, let us look at this example UX equal to 0 its general solution is given by UXY equal to FY where F is any differentiable function because you need to differentiate this and check that derivative is 0 so derivative should exist that is reasonable to assume F is a differentiable function though it does not matter here even if F is just a function not even continuous does not matter because when you write the partial derivatives expression with respect to UX all difference quotients are 0. So, how did we arrive at the above answer it looked like ODE in the variable X. So, AUX plus BUY equal to 0 means the directional derivative of U in the direction A, B is 0 in terms of the notations it is like this DAB U equal to 0 this looks similar to UX equal to 0 UX equal to 0 is nothing but D 1 0 the vector AB is 1 0. So, it is a directional derivative of U in the direction of 1 0 that is the partial derivative with respect to X. So, of course DAB U equal to 0 is more general than UX equal to 0. But important thing is that it is a directional derivative we know the directional derivative is like one variable derivative. It looks like one of the other variables is not there in the equation exactly like UX equal to 0 Y is absent. So, in this case we have to find out what are the variables one of them is there in this equation but another one is not there we need to identify in this case it is very simple X is there because partial derivative of U with respect to X is there Y is not in the equation that is very obvious here. Now, let us understand UX equal to 0 more closely UX equal to 0 it means that U is constant on every line which is parallel to X axis parallel to X axis means Y equal to constant at the equation. So, solution we saw U of XY equal to F of Y. So, if Y is constant UX is constant. So, in general we expect by analogy in this case U is constant on every line which is parallel to X axis now in this case I expect U is constant on any line having the direction AB. In the case of UX the direction is 1 0 right parallel to X axis has the direction 1 0. So, therefore I expect from this experience that solutions of DAB U equal to 0 are constant on any line having the direction AB. We are going to prove this. So, in the next slide we compare these two equations side by side. First let us look at UX equal to 0 and AB we need to make some special numbers. So, AB we take 1 1. So, now UX equal to 0 solution is FY. So, whenever Y equal to 1 that is a line parallel to X axis it has a direction 1 0 and U is F of 1 U is constant. Now if you take any other line parallel to X axis that means any line having the direction 1 0 will look like Y equal to K for some K and U on that is F of K. So, it is constant on each line parallel to X axis. Now in this case UX plus UI equal to 0 this is having the direction 1 1. 1 1 is this direction the line Y equal to X has the direction 1 1. So, U should be constant along each of these lines parallel to the line Y equal to X. Any line parallel to Y equal to X looks like Y minus X equal to K for some K and U is equal to F of Y minus X. You can check by substituting in this equation that this U is indeed a solution to this equation. So, we have obtained a general solution in the case of UX plus UI equal to 0. So, we need to find what that is we got from AB equal to 1 1 if it is general AB what will this be we will see that formula. Now how do I extend these ideas to linear equations but with variable coefficients how will we do that? So, what to do that is the first question. So, notice that for every point in omega 2 this AXY UX plus BXY UI is also a directional derivative of U at the point XY. But the catch is that the direction depends on the point XY it is not constant A comma B as in the constant coefficient case here the direction is AXY comma BXY it varies from point to point this is the difference otherwise it is also directional derivative. Now can we generalize from constant coefficient case and say that U is constant along each line having this direction we would like to say that of course what it means that a line having this direction is questionable because this changes from point to point right in the constant coefficient case it was just A comma B it never depended on XY but now it depends that is why I have put in quotes can we expect such a result? Having this direction means this is a slope Y coordinate by X coordinate B by A that is a slope of the line what line XY is varying B by A will vary from point to point. So, as the direction depends on the point answer to the above question is as the direction depends on the point XY in omega 2 we cannot talk of lines but an infinitesimal version of lines works what is that we are going to present that soon it means that we need to consider curves with slopes B by A we cannot say lines all the time consider curves now lines are also after all curves having a constant slope that is why they are lines but here we have to admit now more general things than lines so we admit curves with slopes B by A that is of course one condition is that we have A in the denominator so we must assume that A is not 0 in the domain let us assume that we will assume that and we will also show that does not make much difference if you have not assumed that A is not equal to 0 throughout it is enough at a point that A is non-zero we know that every point X naught Y naught in omega 2 one of them is non-zero A or B right so we assume that A is non-zero and we can do the things if A is 0 we will work with B so that can be done. Okay so this means what curves with these slopes means you have to look at solutions of this ODE this is the slope of the curve at a point X Y and that I am saying should be B by A. So if B and A were constants the solutions are straight lines so now these are curves so d Y by dx equal to B X Y by A X Y okay so we have got hold of analogous things to straight lines which are curves with slopes B by A okay so we assume that A is not equal to 0 on omega 2 we will come back to this discussion after we finished doing this analysis okay where we say that does not matter you do not have to assume that it is non-zero throughout omega 2 because of certain things which will come into the analysis soon okay there is nothing that you gain by assuming that A is not 0 and throughout omega 2 we will come back to that. So let zeta be a solution to this okay defined on some interval J in X okay whenever this is a solution one observation is that U is constant along this curve X, zeta of X X, zeta of X as X varies describes a curve and U of X comma zeta of X is constant whenever zeta is a solution to this ODE we can verify that so d by dx of U of X zeta X we want to compute this now X dependence is there in both the coordinates here as well as here both the components so first you have to differentiate U with respect to X and derivative of X with respect to X is 1 then differentiate U with respect to Y and differentiate zeta of X with respect to X that is what the chain rule says okay so that will give us a zeta dash of X d zeta by dx through this dependence we get this. So as I told you chain rule will keep coming definitely throughout this lecture on the next one but chain rule if you remove then I think you cannot do PDE so we can we may also say that this is one of the most fundamental results in differential calculus it does not look like a big result to us but it plays a role everywhere okay. So question good but tell me how to get a formula for solutions okay you have observed that if you have a solution that will be constant along curves which are solutions of this ODE fine but from there how do you get formula for the solution that is a question the answer is that do not worry using this family of solutions to one because it is a ODE right so its solutions will be a one parameter family so using that family we convert our PDE into ODE okay we convert our PDE into ODE and ODE is may be solved to get solutions. So now you are as good as your ability to solve ODCs we will do this shortly of course this assumes that you are able to solve this equation one get that family and then converting the PDE into ODE is very simple and your ability to solve the ODE it hinges on that but definitely there is an algorithm okay. So we follow a common strategy to solve L and SL because as we observed the LHS in both the equations and L and SL are is the same both are the same. So now we have to do what is called change of coordinates sometimes called change of variables. So suppose that we have a change of coordinates from x, y to xi eta and vice versa change of variables always like you are going from x, y description to xi eta and you should be able to come back only then it is useful otherwise things are lost okay. So change of variable always both sides and vice versa given by this. So xi equal to small phi of x, y eta equal to small xi of x, y and x equal to capital phi of xi eta y equal to capital xi of xi eta it is very important to write this kind of setup whenever you do change of variables so that you will not have confusion. This is another part change a chain rule will be used chain rule as such is easy okay very easy you can apply but here when you do change of coordinates that is where your real test of understanding will come and to be careful better you always use this kind of notations okay. Normally people write xi equal to xi of x, y eta equal to eta of x, y avoid that that is the first message okay. So this is the change of coordinates obviously it means that a certain domain has this change of coordinates in R2. A function now under this change of coordinates u of x, y gets transformed to a new function call it new function new notation w of xi eta do not call u of xi eta that will cause confusion w of xi eta and vice versa of course by this formula u of x, y right but x equal to phi xi eta y equal to xi xi eta so you substitute you get a function of xi eta similarly here u x, y equal to w of phi x, y xi x, y. Now we illustrate this in a picture see here we have the rectangular coordinates x, y and we have gone from here to xi eta coordinate system through these functions small phi, small psi xi equal to constant of this blue curves eta equal to constant of this black curves. From here you can come back via this transformation and if you have a function defined from here x, y thing to R you can define a function from xi eta description to R okay. Basically it is the address that you are changing with respect to the new coordinates earlier to describe a point in the plane you are giving a x address and y address x coordinate and y coordinate. Now for example you are using a different coordinate system if you want to describe this may be eta equal to some number c1 this may be xi equal to some number c2 so c1, c2 will uniquely fix you for example look at our globe you can easily give coordinates of any location using the longitude and latitude numbers right. It is exactly like that so it is a different change of here it is a change of coordinates so you need to give address fully full address okay. So how PDE changes under change of variables very important we need to do that so AUX plus BUY BXY UI is our LHS in both L and SL equations. Now we will change it to xi eta coordinates very easy we have to look at the relations that we have between U and W and differentiate and find out what is UX what is UY substitute for UX and UY similarly for X and Y here you substitute then you will get the new expression. So UXY, UX is derivative of W look X appears both in this location and this location so differentiate W with respect to the first variable which is xi at this point phi X, Y, psi X, Y, phi X, Y, psi X, Y and then differentiate phi with respect to X at the point X, Y then differentiate W with respect to the second coordinate that is W eta at this point phi X, Y, psi X, Y this is chain rule and then differentiate psi with respect to X at the point X, Y. Similarly you do for UY now substitute UX, UY in this expression AUX plus BUY so you get this expression what have you gained nothing because earlier it was AUX plus BUY now you got something into W xi plus something else in W eta now the coefficients are all functions of xi eta you have to convert them into xi eta because phi X is a function of X, Y, A is also function of X, Y but you know the expression of X, Y in terms of xi eta substitute that you get this. So these are the functions evaluated at this points X equal to this, Y equal to this. So we have got one expression in X, Y coordinates equal to another expression you may call this capital A of xi eta W xi plus capital B of capital B of xi eta into W eta. So we have not gained anything but this is where we can play because xi eta is something that I want to make a choice so that it will be useful for me convenient to me. In fact we wanted to convert to ODE so we would like to remove one of these derivatives how do I remove one of the derivatives just ask that xi eta should be such that this guy is 0 or maybe this guy is 0 then it becomes a ODE in one of the variables that is the idea. So choose xi so that this features only derivative with respect to xi, I decided to let only derivative with respect to xi be there. So that means I do not want this term therefore I demand this guy is 0 choose xi such that this is 0 this forces xi to satisfy this. Of course if you have said there is I do not want derivative with respect to eta you would have said this is equal to 0 but if you see equation is the same right A phi X plus B phi Y equal to 0 so equation is the same equation okay. So let us find a xi with this property now this is also first order PDE right we are trying to solve one first order PDE we ended up with another first order PDE. So what have we gained thankfully this equation is a homogeneous equation so that helps us right hand side is 0 linear homogeneous how does that help? Earlier we observed that every solution of this particular equation is constant along solutions of some ODE which is this we observed this. So from theory of ODE's we know that solutions of the above ODE this ODE form a one parameter family. So assume that solutions are given implicitly by eta of X Y equal to K where K is a parameter. Why one parameter family because this is the first order ODE one initial condition you give and you get a solution that is a parameter okay. Same thing we can express differently but that is why I am assuming that they are given in this form. Once you have this form you set psi equal to eta psi of X Y equal to eta of X Y so you know psi now now you need to still find phi. So you have set psi like this it means your PDE the transformed equation is good because you do not have this term okay but phi is still there. So we need to find phi only then we will have a change of coordinates we will do that. Now having chosen psi choose phi to be a C 1 function such that this Jacobian is never 0 the Jacobian is never 0. The Jacobian condition above will guarantee that this function X Y going to phi X Y psi X Y has a local inverse and phi I psi being C 1 functions the inverse will also be C 1 function that means we have a diffeomorphism. So we have to apply what is called inverse function theorem therefore this is the second most important theorem in differential calculus of multivariables inverse function theorem which is equivalent to another theorem which is called implicit function theorem. You can prove one from each other so that is why both are equivalent and you must be thorough with application of these theorems how to apply these theorems. So the inverse function may be expressed now that X as a function of xi eta and Y as a function of xi eta you can do that. But if you look at the inverse function theorem the assumption will be at some point X 0 Y 0 Jacobian is non-zero then a neighborhood of X 0 Y 0 you have this as a diffeomorphism. So inverse function theorem conclusions are what are called local even if you have the Jacobian everywhere non-zero you cannot say that throughout the domain X Y on which this non-zero this defines a inverse function diffeomorphism you cannot that is why local inverse is always a conclusion from the standard inverse function theorem. What is local inverse it means each point there is an open set on which the above conclusions hold and the open set need not be omega 2. Thus the LHS of both L and SL which is here AUX plus BUY becomes this okay where we are just writing where these coefficients are evaluated at they are evaluated at this W xi is at xi eta. So the right hand side is function of xi eta.  Therefore this LHS of L and SL become simply A xi eta W xi of xi eta. So no eta derivative here so it is going to become ODE. The linear equation now becomes this this is LHS right hand side C of X Y you express as xi eta by this change of variables use W and D also you express using the change of variables D of X Y capital D of xi eta that is a relation. Now you may write it like this it is a ODE right it is a linear ODE therefore it can be solved. Now let us see what happens to semi-linear equations. The PDE will transform to this because right hand side there is nothing to do much it is just C of small C of X Y U earlier now it becomes capital C of xi eta W. Now you write like this and the equation is non-linear ODE. The ease of finding a solution depends heavily on the non-linearity the capital C and capital A. But we know that it has solution as the right hand side is a local ellipses function solutions are there. Once the function W is determined function U is known now we know right the correspondence between U and W. Now small remark on our assumption that we assumed this right A is not equal to 0 on omega 2 and one more thing we assumed on the way after choosing psi we said choose another phi C 1 function such that the Jacobian is never 0 on omega 2. However we met inverse function on the way that theorem even if you with go with the global conditions like this this one it will give you only local conclusions there is a problem of the inverse function theorem. So we did not gain much despite our global assumptions that tells that there is no need to assume globally. Assume that A is non-zero at some point x naught y naught and the conclusion that you get will be in an hybrid around x naught y naught. In any case even if you assumed A is not equal to 0 in omega 2 when you went to inverse function theorem it only gave you conclusions around the point x naught y naught. So as a consequence the change of coordinates you will find in a neighborhood of that point whichever point you have fixed here I have fixed x y. So but there are also global inverse function theorems this is just for you to be aware of global conclusions are possible from global inverse function theorem. For this I refer you to this book of multivariable real analysis volume 1 it is called differentiation it is authored by Wister, Matt and Kolk they also have a second volume which is about integration these are very slightly fat books but they write very nicely. So let us now specialize to constant coefficients. So solutions to d by d x equal b by a because we have not yet solved a u x plus b u y equal to 0 so far now we are going to solve. So equal to b by a are given by b x minus a y equal to k where k is a parameter choose psi as b x minus a y okay solutions okay ad y equal to b dx so b after integrating you get b x minus a y equal to constant that is how we get psi. Now you have to choose phi the only condition on phi it should be a c 1 function and the Jacobian non-zero. So this is the Jacobian psi I know the derivatives I have put in here this is psi x this is psi y you want this to be non-zero in this case there is a easy choice for phi it is a x plus b y what is the relation between like a x plus b y equal to constant and b x minus a y equal to constant they are perpendicular they are like x axis and y axis right okay so note that this change of coordinates x y going to a x plus b y b x minus a y you may call this as psi equal to phi of x y this is eta equal to psi of x y these are global it is an invertible it is a linear transformation not to it is a invertible it is global this is linear no linear if things are invertible you will get global. But in the general situation these are non-linear equations okay special case of constant coefficients let us continue the equation a u x plus b u y now becomes a square plus b square and w xi equal to 0. Now I need not even bother to change this into some new coordinates because this is non-zero right you can cancel and conclude w xi equal to 0 and solution it means it is a function of eta alone right w xi equal to 0 it is a o d e you see from a u x plus b u y equal to 0 we have got a o d e w xi equal to 0 of course after change of variable. So this implies that w is simply a function of eta now what is eta we can substitute back get the u u of x y equal to w of phi x y psi x y but w I know is only arbitrary function of second coordinate that is f of psi of x y and what is your psi of x y b x minus a y. So you just connect it back to our original equation u x equal to 0 that example u x equal to 0 equation means a is 1 b 0. So therefore it is arbitrary function of minus y arbitrary function of minus y is same as arbitrary function of y so we got back. So observe that solutions do not depend on the choice of phi at all. Now you see b x minus a y equal to constant the function is constant on that line. So this again means that u is constant on any line which is having the direction of a b. Now let us look at an example x u x plus y u y equal to 2 u here I have said using change of coordinates reduce this equation and find the general solution. So this is a recall of the change of variables we have to do this and then go on substitute for u x u y expressions inside this get the expression x phi x plus y phi y w psi plus x psi x plus y psi y e w eta now set this equal to 0 find solutions of this. So that means divide by dx into y by x and solutions are given by x by y equal to constant that is a family therefore psi of x y is psi x by y now we have to find phi choose phi equal to y and Jacobian condition will be satisfied. So we have got now psi and eta this is a function of phi of x y eta is a function of x y psi of x y is equal to x by y and then you get the relation between x and y and psi and eta then the LHS becomes y w psi because we made sure that w eta coefficient is 0 so y w psi but what is y y is psi so it is psi w psi is the LHS what is RHS it is 2 u so it is 2 w so psi w psi equal to 2 w. So w psi equal to 2 by psi into w it suggests that we should avoid psi equal to 0 so solution will be this w psi eta equal to f of eta into xi square after solving this. So this is a way to solve using change of variables and then going back to x and y we get u x y equal to y square f of x by y now it is clear that it is defined for all x and every y such that x by y belongs to domain of f. So you choose any arbitrary function that you like of one variable and x by y should make sense that means y should be non-zero and then it should be in the domain of f so you get so many solutions. Now this is another example where the right hand side is u square non-linear equation right but as a PDE it is a semi-linear equation LHS is same so we can skip the computations finally you end up with w psi equal to 1 by psi w square actually what you get is psi w psi equal to w square so I take it this psi. If you solve you get this answer w psi equal to minus 1 by f eta plus log mod psi f is an arbitrary function going back to x y coordinates we get this expression so this clearly tells y equal to 0 has to be avoided because logarithm is there and once y is non-zero it is fine. So and x by y should belong to domain of f so choose any f of one variable function of one variable with some domain and then this solution is valid for all those x y such that y is non-zero x by y belongs to domain of f and log mod y plus f of x by y is non-zero. So domain of u may be written down that is not important one can always write down. So summarize what we did is that linear and semi-linear equations were transformed to ODE's by a change of variables and general solutions were obtained. Two examples were presented to concretely illustrate the general algorithm that we have presented for finding general solutions to L and SL. So in the next lecture we are going to see how these ideas can be generalized or extended to the case of quasi-linear equations. Quasi-linear equations will pose a new troubles we will see how to overcome that. Thank you.


just another case I suppose you'd call it as judge of the juvenile court I've handled hundreds funny though the way you can never get used to them take Edie Adams here she tried to prove she had nerve ran off with a stranger who promised to marry her well he robbed the building loan office the police picked them up and here she is in my chambers a delinquent delinquent in good sense I can't get over it sometimes how teenagers can be such suckers do you know what a sucker really is ask any carnival pitchman the sucker is the guy who thinks he's smart that he's putting something over on you take the old shell game the sucker never wins why because the P is really a ball of wax it's never under the shell it's under the operator's fingernail all right what's that got to do with you you never fell for the shell game don't fool yourselves a lot of you have fallen for it thrown away a future like nothing in the history of the world for what a kick or a flame a thrill you think you're smart enough to get away with it but you're just being a sucker what I call being delinquent in good sense like these two parked on a lonely road just looking for trouble and trouble is there all right if you look hard enough you can always find it especially if you're the sharp one the guy or gal who doesn't have to listen to your parents good sense or follow the rule because you're smart enough to beat the game and take care of yourself that's what this couple thought did you read about the case in the newspapers they found out how it feels to be a sucker too late to do any good but they found out what they didn't know was that men like this make a practice of lurking in lonely lovers lanes to prey on young people who don't know any better than to be there sometimes the victims are lucky they lose only money or their jewelry but not this time we're fortunate to get out with their lives and that's an experience they'll never forget one case and there are hundreds more in my files all normal average kids who saw their lives ruined in a few hours or even in minutes let's take a look at another one Mary Hansen there's nothing wrong with babysitting in itself it gives parents freedom it gives you a chance to make some money and learn how to handle small children that's true so long as you and your parents know the people but Mary put an ad in a newspaper for sitting jobs but the idea of going to a strange home with someone you never saw before just because he answered an ad well it's plain idiotic you wouldn't go away with a stranger for any other reason and just because it's under the guise of babysitting doesn't make it all right but this time even Mary's mother is fooled you see he gave her a phone number where she could reach her daughter anytime an hour and a half past time and Mary isn't home yet about time to call that number he left you isn't it Mrs. Hansen you think it's silly to worry don't you after all what could happen to Mary on a babysitting job but the woman who answers the phone has no family she never even heard of the man or of Mary Hansen no she has no idea where the man got this number and now Mrs. Hansen it is time to worry but I'm afraid it's too late to do any good after letting your daughter drive away with a stranger another headline this one was just last week it's in my files you can read about it now let's take another example Ethel Ryan's case one of the nicest girls in her school like a lot of juniors and seniors Ethel and her friend Lynn thought they were too sophisticated for boys of their own age they wanted somebody more glamorous and the two in the convertible were just what they had in mind to me it would seem that the fact they've never seen either of them before should make a difference well it does to Lynn for a minute but Ethel talks her into it it's daytime Ethel says and aren't they grown up and smart enough to handle any situation Lynn agrees finally both of them got home safely and they're really in luck Lynn tells her mother she and Ethel met two of the nicest boys and they're going out with them tonight who are they and where did they make them Mrs. Coe asks well then explains they don't know their names yet she and Ethel missed their boss then you mean they picked you up and you don't even know them well her daughter is certainly not going out with strangers she may be old-fashioned she tells her daughter but that's fine so Ethel gets the bad news Lynn's mother says no well it's tough but Ethel certainly isn't going to give up a good time even if she has to go alone Lynn wishes she had a mother like Ethel's one who never forbids her daughter anything see you later Ethel says maybe well I wish that we're all there was to it one girl out on a date the other disgusted at staying home but life is not quite that simple when one breaks the rules we pay for it won't soon decides that without Lynn three is a crowd so Tom leaves them alone now Ethel is really on her own I suppose just about here the horse lapses are starting in the audience all right go ahead and laugh of course Ethel isn't laughing she can almost hear all the warnings she never listened to about being picked up by strangers and here's something really funny like mr. and mrs. Ryan and Ethel herself and I can tell you about hundreds of cases I hope you're beginning to get the idea mr. and mrs. Adams are and Edie too she's going to a detention home for three months plenty of time to think about whether a few minutes of showing off or feeling sharp is worth a lifetime of regrets if you're willing to risk that you're not the young American men and women I think you are think it over why not get really wise really have don't be a sucker


Recently, a very influential person, a very huge social media following became Muslim. Alhamdulillah, they knew Muslim. However, he is a man who is perceived as a threat to feminism, the whole feminist project. And of course, a new Muslim doesn't become a Wali of God overnight. The Prophet sallallahu alayhi wa sallam said that none of you become a true believer or complete believer until his hawaa, his passion, his caprice, his accordance with what I have brought. This is a lifelong struggle. But check this out. There was a Muslim sister who tweeted this was public. She tweeted that if this new convert is welcome as a Muslim, by other Muslims, she will lead this law. And she said then I will deal with Allah on the Day of Resurrection. How could she possibly say something like this? Why would someone taking Shahada threaten her Islam? The reason is because it seems to me, I hope not, but it seems like her religion is not Islam, with a dash of feminism. But it's feminism with a dash of Islam. You know, Hindbint Uttabah, Cannibalized, Sayyidina Hamza, and Ghazwat Uhud, Sayyidina Hamza, radiallahu anhu, one of the most beloved people to the Prophet Muhammad sallallahu alayhi wa sallam. And she came on the Day of the Conquest of Mecca and she was veiled. And she came to the Prophet sallallahu alayhi wa sallam and said, praise be to the one who made his religion victorious. And he said, man and who are you? And she said, end. And he said, welcome to the religion. He didn't turn her away. He has no right to do such a thing. Even he doesn't have a right. The Prophet sallallahu alayhi wa sallam didn't want to see the face of Wahshi because he killed Sayyidina Hamza. But the Prophet never said to him, no, no, no, you can keep your shahada. We're cool with your shahada. We don't own this religion. This is our privilege that Allah subhanahu wa ta'ala made us Muslims.


Hey everybody it's Sam at Mixed Up Craft, thank you for watching my tutorial today. So I'm going to be showing you how to make this really fun box card using my tower fold dies. Now I will also share tutorials on how to make this fold without the dies but for those of you that have them this is another really fun and creative way to make some really special cards. So as you can see I've got an underwater theme here and by pulling the sides in and out like I'm doing so it gives the illusion of those creatures moving and they're just stuck there with a little bit of acetate. In the back you've got the crab with the holographic shell and then on the front here you've got the treasure chest which looks really really good and then the whole thing will fold flat like so. I'm fitting to a 5x7 envelope or you can use one of my box envelopes and I'll link that along the way and then on the back you have lots of room to be able to stamp and write your message as well but I think it looks great. When it's opened up it's just got such a nice look and it's a really special card so let me show you how to make it. Okay so this is the die set that I'm using since it's the 5x7 from the terrific tower die set but you can also use the 6x6 and I've done a craft world exclusive video using the 6x6 with a similar style so I'll link that one up here and it'll also be linked in the description box so you know you might have the 6x6 size and also I have the landscapes. This is 5x7 but you have this panel here so it'd be a good one to cut an aperture out of that one you can see the landscape panels as opposed to the 5x7 where you've got the portrait panels like I said I'm using this one today because I wanted to have you know this tall kind of area where all the fish would be swimming so I've already gone ahead and cut everything and like I said at the beginning you can make this without using the dies I have the tutorials I have the tower fold playlist I have a look there but I have used the die here so this is it it's really really easy to use and it's just nice and quick so what you want to do is die cut two bases so I've done one here in the white so it's just simple pass it through your machine and you will have this one cut then you want to cut another one but this time you want to cut the middle out at the same time so you can see there that sits perfectly over the top then you've also got a mat and layer in the set you want to use the smaller mat layer so if you're making this yourself you'll just need to find something that you've got that will fit within this space but you can see there that fits perfectly so when I was laying this one down I just used some of my washi tape make sure that you've got an even border at the top and the bottom and also the left and the right so that when you you know it's all cut through if you can cut it all at the same time you can see there we've got this even top and bottom and we're going to reinforce that slightly when we add the acetate behind so then I've cut my mats and layers so I'll just explain these ones so this one here is the largest mat so it's this one here and that's going to go on the inside which is going to be on this one here and it's just going to stick in the center there okay once I start putting this all together it's going to make sense but you want one for the inside these ones I've done four so I've got two for the outer sides and also on the back side just so it looked nice now you you get your mat and layer for the side pieces you can see there's the mat and then the layer is slightly smaller I've just used the largest I've just used the mat layer so whether you're using the 5x7 the 6x6 or the 7 or the 5x7 landscape they will all have those mats and layers so you can decide but I've done four of them and then I've cut this panel using the same paper and this one here will cover all of these panels so if you want to cover every one then you'll need to run that through four times and it will give you 28 pieces okay I've also then cut a mat and a layer using those two here for the back so that's where I'm going to stamp and write my message and then I've cut a piece of acetate which is going to fit behind your aperture so whatever size you're doing you want to cut your acetate so it's going to cover now I've already put red tape very thin layer of red tape you can see now that's going to cover to look like the fish tank the fish bowl you know whatever you want to do here so before I stick all those pieces down let me show you how to pop this out so I'm going to do it on the plain one here it will be the same on this one but for those of you that maybe haven't seen this card style what you will have is when it die cuts you'll have score lines along every other so there's no score line here but there's a score line here then it misses one there's another one misses one there's another one okay so with every one where there's a score line here facing you you want to lift that one up towards you then miss one and bring that one up you see I'm kind of putting my finger there I'm using my finger underneath to pop it up now as you pop those ones up it will all come into play these ones behind here are going to go down so you can see although it hasn't got a score line here it has one here but then this one doesn't have a score line there because this is going to be your piece that will be seen from the front so you don't want there to be a score line there so it just looks neater basically so that one can then go down again go down and as you work your way along it will start to come into this shape here now there's also score lines through the middle here you just want to start working in those score lines as well so I like to just feed my finger through and it kind of you know these ones come this way and those ones go underneath like so and then I just kind of bring it down and fold it towards me and it will start to find those score lines here and just go along and just pinch those ones because you can get right in there now and then just bring that over and then I can just burnish all of these sides here and then I flip it over and just do the ones in there as well I am using a thick cardstock this is 300 gsm but it still works and then you just want to repeat the same on this side so again I've got the score line facing me there so I'm bringing that one up and down up down up down it doesn't matter which way you do it I mean you do want to kind of follow the score lines because we put them there so that then you don't get the score lines here however if you did do it the other way it's not the end of the world but do make sure that they're the same on each side so again just go pop my fingers in push that down just find the score lines there okay so now you have your tower fold and that is what this die creates it's this shape here you then have these edge dies that will coordinate so this one here coordinates with the 5x7 landscape but you could use it on this 5x7 if you wanted for this one you have the balloons the stars and the flowers so basically this border then can attach onto the sides and I've got all of that on my release video which I'll link up here if you wanted to see that in more detail and then that's the one for the 6x6 and it's got this beautiful bow it's really popular and you've got the butterflies there and the hearts it's just a really pretty set so you do have coordinating edges if you want to do but for today's one I'm going to use it without the edges and I'm just going to use the mats and the layers so now I'm just going to do the same as what I've just done there on this one okay so I just started to do on this one but I think because this is obviously at the moment it's quite weak I think it's going to be better to attach this piece first and then do the folding so I'm going to remove the backing okay and then very carefully just sit that down so I'm going to bring it right up to the top there so now that's just made that very strong again so I would advise if you've cut a large aperture out of it like I have then add that and then do the folds okay so I'll put those both together so what will happen when we do go to stick them together is you're going to stick one over the top make sure again they match up like so and now we can see through this whole section so once you've got them that way you could stick this one in because this is going to go on the back but I think I'm going to do a little bit of inking and stuff with that yet so I'm going to leave that there but you can see how that's going to work and already it's starting to give us a really great effect but I am going to stick all the mats and layers down on the front so I'm going to start building that up with my stamped images so I'm going to stick one of these either side like so and like I said all of these on these pieces here now you can just flatten this back down and what I like to do is just with some glue a little line of glue like so do like a bunch at a time and then it's really quick to just stick them down this is because I'm covering every one I just want to do it like so that's if you want to cover every one if you want to do every other then you can some people just like to do the fronts and not even do the sides so it's entirely up to you but I'm going to go and stick all of this down okay so I've stuck everything down and I've also added this very thin frame and you can do that with the mat and the layer dies so I just pop them together like so if I flip it over pop a bit of washi tape just to keep them so that you have a perfect frame and run it through your die machine in your chosen color and it will give you that very thin frame but I just think it works quite nice so I've just done it in the same blue that I've got for the back for my mat and layer and then I have all of my elements here so I've used a mix of really of all my kind of underwater themed stamps and dies so I've used for the sentiment I've got birthday fishes which is that one there and that's from the paper discovery underwater world then I've used for the I always love this one the little treasure chest and I've got all the glitter on the top there and that is from the hunky dory for the love of stamps under the sea I will link if I can find these some of them are older but some places do still stock them and for the the kind of treasure look I use this cosmic shimmer and it's the blush haze and it's gorgeous look at that it's just got so much shine and then for the fish and the starfish and the crab I've used this one which is paper discovery underwater world so they kind of work together this is paper discovery and I used this one I've used the for the shell I was that one there and I've just died cut that in holographic cards that catches the light nicely and then for all of like these pieces of seaweed and stuff I've used this one here so I've used these ones which was the paper discovery beyond the sea yeah it was for those but also I use this one for these bits I have them still in my dye machine and that creates all of these bits of seaweed as well but like I said I try and link as much as I can and then I've created the seabed here just using a piece of scrap card stock I've just kind of inked the edges there to darken them up and then I've used the this is the gravel paper discovery and bottom folder but I thought it kind of looked like sand and stones and things like that on the bottom so on this piece here which is going to be the inside I want to start building my scene so I cut this using the same dye but just obviously just at the end of it so I'm going to stick that one down the bottom there and then I can start creating my scene so you know got bits of the seaweed here I think I'm going to have this one like so and then maybe have the crab so he kind of like covers the ends of the seaweed there I'll pop him on some foam as well like so and then I think I'll have some more seaweed coming in from the top so I'm going to stick these down onto this piece first and then I'm probably going to have some decorated on the actual front on the outside of the card I know the whole point is like everything's meant to be inside the tank but it's quite nice especially in a card form to have things it just makes it a little bit more tactile and maybe we'll have this one here just so they're kind of creeping into the the scene there something like that and then if you start to like lay things down so if I just put this then you can kind of lay it all in there just to kind of get an idea now the fish are going to be attached with acetate so that they move so you want to kind of place where you want them now the acetate needs to sit it's going to be the same width of this and we'll cut that before we stick the two together but you do want to do this decoration first but if you place them so if I'm going to have my seahorse here my acetate is going to come out from this one so he will float and then I think the fish would sit nicely on that one so he can be up there and they actually have the room to move within the card so I'm going to have a piece of acetate there and a piece of acetate there so I really like that scene there and then I think I'm also going to bring in the shell just behind him then when you stick this on the top you want to make sure that the same bottom is the same as the back one there because they do have a slightly different top to the bottom so just make sure you'll know anyway because it will all sit perfectly but you can see now what we've got and then I'm thinking about having a little cluster on the front here take the end off of that one because I like to get everything placed because then I know if I need to cut anymore so I'm going to do this on this side because I've got everything in there on the left so I'm going to have this on the right and then we've got a few more bits and pieces so again I'll build them up and then I think I'm going to have the treasure like so with maybe the sea um the starfish just next to it so I kind I like that placement and then my sentiment I'm going to stick using some foam on the very top there so you can see everything going on um and I think it looks really good so I think before once I've stuck this down before I put that on top I'm going to use the glossy accents to just um add in some bubbles which I like to do when I do any of these kind of cards so I'm going to start sticking it all down I'll come back when we do this and then we can add the top and the acetate okay so everything is now stuck down apart from my fish here so you can see that if I just bring it up I also put this on some foam so I could tuck bits of the seaweed in behind it just creates some shadow and then again if I just bring out the front there that little cluster I think it looks really cool so I've cut a strip of acetate obviously your acetate is going to vary depending on um you know what you've got attached to it so whatever the width is though you need to the width though you do need to make sure it's obviously going to fit within the sections here so I need to remember which one I said yeah so I can see there that that's going to fit perfectly so I'm just kind of hovering it just kind of sit it on top of that section there and then you should be able to rest whatever it is that you're going to have floating so you can see that's rest and now when we move the side of the card it's going to move now you want to make sure that when you fold it flat it's still going to sit within that section if you go too long obviously it's going to hit this when that comes down and it's just going to hit this side and it won't fold flat but that actually is a perfect so I'm just going to it's a perfect length so I'm just going to snip that off there and I can grab some of my red tape and I'm just going to pop it on too so again I can see yeah it's going to sit there so I'm going to pop my tape on that area there but hopefully by showing you how to do it you can easily then adapt this you know for your card and then I'm going to do it on the other side as well always use a red tape when you use acetate because it will stick really well so I'm just going to take the backing off of one side and then again it was that one there and then just stick that within there so I've then got my backing on the top side here to peel off in a minute then for that bit there I'm just going to pop just a small strip of the red tape just on the end and that will be plenty for you to attach your element there okay so I'm just going to grab that other piece and I'm going to do the same with the fish now this fish is a bit longer so again I need to make sure that whatever he's attached to when he folds flat yeah he's going to sit within that section so again trim that off and I'm just going to do the same again so now I'm just going to attach the seahorse and the fish okay so now again before you stick everything together just place it over the top just so you can you know make sure you're happy I might move my sentiment which I still can just because he's kind of just in the view there of that fish but look how cool that looks I think it looks wonderful so please with it yeah I think I'm going to have my sentiment I don't know need to play around maybe I might have it like here or something on an angle okay so I'm going to take the backing off of there and then you want to add your glue I'm using the clouds this is just going to strengthen this so much and just pop the glue across all of this area obviously don't need to worry about that because I've already got the double sided tape see the glue coming out there there we go this glue gives me a little bit of time as well so because you need to do both sides at the same time some of your you know your white glues might dry quite quick start from the bottom because you want to make sure it's going to stand up straight and obviously once it attaches to that little bit of red tape that's in there that's going to obviously stop you being able to wiggle it around so I'm just going to make sure that's okay and then I can just really push down on those bits there and if you actually fold the card flat you'll be able to really push in on the red tape on those two there you can still wiggle a little bit around the top and the bottom there just make sure all of these bits that you just pinch together just to make sure that glue secure I'm just going to keep it flat just whilst I push down on all of those okay so I finished the card so I've ended up cutting the sentiment into two so I just like that little arrangement there and then I've also added this starfish which is from the same stamp set just to kind of balance out everything it needed something on this side and I quite liked having this outside and I popped on a little bit of foam but now you can see how cool does that look I absolutely love this thing it looks brilliant I haven't put the glossy accents because when I was doing it I realised that they are actually obviously quite far away from the back there so I've just left them out but if you wanted to and I will share my kind of undersea playlist and you'll see I use that a lot if you did want to use it and then on the back I've added my mountain layer there as well so that's ready for me to write my message and then the whole thing will just fold flat and that will fit into a 5x7 envelope or you might find one of my box envelopes will be better because there is a bit of dimension and there is a bit of bounce to these cards as well when you double them up and I'll link the envelope boxes there so I hope you've enjoyed this tutorial for those of you that have the dies I hope it's given you more inspiration on other ways to use them and I can't wait to see your versions and what I'll also do is I'll link up some other cards that are similar kind of underwater themes that you might enjoy and if you haven't subscribed I'd really appreciate it if you did enjoy today's tutorial just click on my face there and hit the notification bell and then you'll be notified when I next upload a video so thanks for watching and I'll be back again very soon bye


Hey guys, welcome back to another college week in my life vlog today. It's Tuesday I'm proud to be vlogging Tuesday through Friday Tuesday through Thursday My school week is Tuesday through Thursday. If you guys are new here. Hi, I'm Kimsey I make a lot of lifestyle vlogs. I go to Zoe leadership college, which is accredited through South Eastern half internship half college I've really learned how to explain this better When I graduate I will graduate with a bachelor's in business administration. If you guys are new here subscribe It's currently like 6 20. I'm about to head out to Hop Pilates class. I take Pilates at 7 Tuesday and Thursdays So these vlogs are a lot of them start off the same way I'm wearing this which are probably to wear actually today just over my like workout stuff but hope you guys enjoy this vlog and Yeah, let's get started. It feels so good outside right now. It's 6 22 about to leave I have all my stuff for class in a ritzia box. It's my friend's good stuff delivered here. It feels amazing Guys look at this right now. Oh my gosh. Hey people. Good morning. We're walking to Starbucks right now It's like a 15 my favorite Pilates teacher asked me to private tank with her today It's a big day for me. We're going to Starbucks. I feel very cool right now We're going to Starbucks I'm getting my new favorite drink. I'll show you guys So good Okay, thank you. Also, I love the colony cups this year. How are we feeling about them? Okay, this drink It's not on the menu. I ran into my friend who's literally at Starbucks ordering this from our instant stories and wearing an old Twitter of mine, but um It is the sweet cream cold beer with peppermint syrup not vanilla. It's so good Quentin hates it because he hates peppermint, but I love it. All right everyone Chinking cold brew we ran into so many of our friends. We're so popular I'm really having the best day ever now that daylight and I are gonna train together I originally said no because I'm gonna be traveling like I'm only gonna be in just in LA I feel like a week and a half in December two weeks Two weeks. Yeah two weeks. We're going to Texas for Christmas for two weeks as well. Oh my gosh guys look Jeffrey star and Shane Dawson billboard right there. Do you see it? Currently on my lunch break.  We're just doing homework majority of the day Okay guys, so I'm out of class for today. It was really fun We have her night this week, so it's a pretty big week Which is like our women's gathering, but it's like one of the biggest things we do all year It's so much fun. So that's on Thursday. So I was editing some videos and stuff for that for Zoe Drink class. I did some homework. I eat my salad, but I have a recording. It's 3 p.m.  I'm a cha-cha matcha. I'm about to go in. I need food. I need matcha I actually haven't been I feel like I haven't vlogged here in like two weeks It's pretty long for me. So we're gonna go do that and I'm gonna also Bring my books to read My iPad and my Bible and my journal of my book book. I guess I left it home. That's weird I never do that, but that's fine. So I wasn't gonna read that. Um, oh my gosh. This is so cute This is from our ZLC retreat 2019 they gave us these booklets Like my program went to Big Bear for the weekend Literally the most fun weekend. I think I've ever had like my favorite weekend ever And it's like all of my notes and stuff from that and it was 90s theme. So it's like gel pins.  So I'm going to Go I have this huge trash bag and Quintin left me a Fiji water bottle He doesn't know that he left it for me, but he did so yeah, I'm gonna go read Listen to some music Gets Macha. I'm very excited Here we are back to my favorite place My iPad is about to die. So that's great, but I'm sitting at Chacha Macha. It's so cute and my nitro latte It's one of my favorite drinks in the entire world, and I got these power bowls, but I already ate them so you can't really see them Those are really good Quintin's like obsessed those This is my favorite drink ever guys speaking of drinks like we literally posted this on stories yesterday today today really and You guys are already Getting so many there's more, but that's just so funny. Also, you guys don't follow me on Instagram It's just at Kendiel Elizabeth. It's super cute. Also, if you don't follow that, I do so much podcast Instagram It's really funny There's this Kendiel Elizabeth starter pack and it's like my friends in real life. We're like that is just so good It's just so funny. So I love that It looks like I'm bald with my vlog camera right now, but it's fine. Okay Hey guys, welcome back to the I Love You So Much podcast It's me, Kendiel Elizabeth and my producer Taylor I always always when you say your intro go along with it in my head too because I know it by heart Well, honestly just now Did some grocery shopping. I was sitting at two girls on the go got two bags I'll show you guys a mini haul of just new things that I'm trying Because I get the same stuff too much like every week, but I'll show you guys some new stuff All right guys overview of my normal stuff. I just made the counter so messy because they spilled some stuff Pasta broccoli kale gluten-free bread apples banana salmon Okay, soft mango. This is one of the things I want to talk about one of my favorite stocks I haven't bought this in forever. I'm sure it's not great for you, but it's so good Another thing that is a Trader Joe's staple that you must get the dark doc. What's the dark chocolate peanut butter cup? Put them in the fridge. They're even better. Okay. Also. This is how you know that you're dating Quinton one because This is like his snack selection at house, and this is like pretty much all he eats But also I'm such a great girlfriend everyone. Don't you think anyways? I got these I'm pretty sure That Brooke talks about them in her videos, which I don't know how I know that someone said that she talks about them Maybe I'm totally getting this wrong, but I'm literally Brooks number one fan So I don't know I missed it, but here's the thing part of me thinks I did see this in her video I don't know. I honestly cannot remember. I just feel like she does talk about these But again, I'm a number one fan. So yeah, I don't know. So they're like turkey sticks. That's a beef stick That's a turkey stick. Apparently they're just really good to hold you over So I'm gonna try them out. I got two different flavors. That is what I got I'm gonna go shower and then cook really quick Quinton is almost here. All right guys I'm out of the shower. I just changed into sweats a gray t-shirt and of course my ex uppers Um, I need to put that jacket away, but I was gonna do these summer Fridays jet-lag masks But it's gone like missing. I normally have it in one drawer and it's just completely missing Also guys look at how cute Coco looks right now because she got groomed so she's so pretty Right Coco. Oh my gosh.  I'm filming a haul for them very soon But I'm so excited for all my new clothes Sneak peek at my princess Polly haul these really cute boots I've only always almost picked them up on the site, but I haven't yet and then I have a lot of clothes I think I have one more package coming in For the haul and then I'm actually gonna be working with Glossier on a video I think in December, but they sent me product, which is very exciting. I've never been set product by them But I'm actually so excited. They have a face mist. I'll show you guys all this in the video, but cannot wait guys I just made dinner. I talked Quentin into letting us eat at the couch instead of the kitchen and table, but This is what I made for dinner. I can't believe I'm such a chef now salmon, sweet potatoes, broccoli Nutritional yeast and organic tahini. It's really really good. So after chef kins Exactly your fires are a game changer.  Yeah linked below Good morning everyone doing my Collagen and my coffee All right guys. Good morning. Um, I and just I actually get ready on Wednesdays Or I try to because I don't have to go to an early morning workout class because I go Wednesday nights So this top that I'm wearing is from Princess Polly. I just got it last night wearing my Levi's Favorite denim that I own. I need to get more Like I need to get more good genes basically like that's my next thing These boots are Steve Madden. I Know I think they're like Prada look alike They're super cute my sister wore them last one turn that I bought them and she got really mad at me And I actually don't wear them that often I kind of forgot about them But super cute and then I just have this coat that I'm going to throw on This is awesome. No that I got from Princess Polly. This is the outfit and I'm just wearing the coat I like the neon pop super fun and very trendy and then my instrument for Fisher hoops that are the best I'm believe these are the Baby Samira or the mini I always get so confused because like baby man I don't know. They're like still kind of bigger, but they're like a good medium everyday size and they're so light They're definitely expensive. I recognize that but I'm someone who would like invest I'm gonna wear it every single day and these are just like so lightweight You don't feel like you're wearing them like you know when like your ears start to hurt I can wear these for like 15 hours and not feel anything and they're just like next level So that is my outfit for today I'm about to head out to Class and I'll talk to you guys in the car. So I'm on my way to class I'm listening it to dax shepherd's podcast with kid hats. It's really good But I think I'm gonna stop at Starbucks because yesterday I don't even if I said this but my entire Starbucks order was free like the whole thing Which was like $15 that's getting copies for other people and then I have money in my card So I'm like why not and I kind of want kind of with the peppermint culper that Morgan created It's literally my mentions are flooded with you guys getting them. They're so good So I think I'm gonna stop and get one just because I'm gonna get to class like a little bit early So I might as well, you know, I got my Starbucks order ran into Quentin, but This is actually really good. I got a venti today. It's got a lot to do. All right guys day Three of this week getting this drink. It's really good You'll really like it Also, I need to be in class in 15 minutes with this is the podcast episode I've been listening to you today Let me know if you guys want me to do like a series on Instagram of like podcasts I've listened to each week I can post them like every Friday and then you guys gonna skip through and then out into a highlight or something I don't know how that would work. Just let me know what you guys think Hi, everyone. We're on lunch. I Don't know how you're directly. I just walk around things on I've summoned Dom to take an Instagram photo of me since I'm not wearing socks today. Yes. Thank you It really has been a while since you've taken a photo for me, so we're on our lunch break, but we're working in the office I just ordered tender greens Very exciting everyone No, I don't All right Update on the photos everyone Dom killed it. I'm a woman. She's very efficient and very quick Which I appreciate other people are not I just want to get back to my spinach and artichoke reduce skill dip from Trader Joe's It's actually my new thing right now. No, a lot of you guys are on your peppermint grind You guys are on your chick-fil-a cold brew grind, but I just want to let you know no no chick-fil-a We canceled our chick-fil-a cold brew. That was your fault. I'm giving you ownership that anyways So I know you're on your peppermint cold brew grind, but really you gotta check out spinach artichoke dip reduce skill from Trader Joe's It's actually freaking phenomenon. There you go. So check it out Can't miss it. This is really hot guy coming up, but I look like I see him. Oh my gosh All right guys great day at class. I'm actually on my way. I got out a little bit early. It's 2 30 I'm on my way. I feel like there's something on this lens, so I'm so sorry But I'm on my way to join the juice to get some work done And then tonight we have our workout Wednesdays, which are new tradition at Wednesdays on sunset to meet Morgan Quinton We have some new people joining us today So I'm doing Pilates with Val who's also going to join the juice and then Quinton's also joining us tonight for my favorite instructor daylight and daylight is very excited Hey guys, I have all my stuff and I'm going to Joe and the juice to get some work done I was here last Wednesday before our Wednesday workout. I built Lulul not Joe though. Joe and the juice One last look at my outfit today because I'm not wearing sweats Round of applause for me. Um, so I'm working in I've been working here to join the juice for a few hours I'm going to change then take a conference call in my car and then go to Pilates I'm going to change it to my Pilates stuff now. So I don't have to change there Yeah, all right guys changed into my outfit. I have to wear grip socks And there's something going on over All right guys, I just had a call with my producer Taylor I take a lot of my business calls in my car either at my desk my officer in my car and we just went over. Oh my gosh guys There is this one promoter He literally didn't even like okay. There's this one promoter who always even like dance me I don't know how we got I don't go out.  Let's see he emails me He DMs me all the time and like he's like nice. I'm just like whatever like I don't ever like answer You can like go through our DMs, and it's like slide slide slide, but he just said hey ariana To in this DM not even hey Kenzie so No, like no answer me has any desire to do that, so it was how to call my producer Taylor We were going over the podcast They sent me a report. So we were just like doing all that stuff. Anyways, so Pilates is in 45 Val and I I think They're just gonna go sit outside in the parking lot here. It's such a beautiful view Oh my gosh guys for a hot Pilates Quincy's back Okay guys, we're at sweet green Yeah, it's our Wednesday tradition back home I just showered I'm already ready for tomorrow morning Pilates at 7 a.m. So I'll see you guys Good morning, everyone. It is 6 24 a.m. I'm on my way to Pilates. I left to come back Yes, so I'm taking a 7 a.m. Class after that we have a chapel with class which chapels this morning Normally of class until 3 but we have her night tonight. Her night is one of the most fun things that we do it So it's the big girls Fun service thing. It's really cool. Everyone gets like a little bit more dressed up There's like photo booths. It's a really great service of really great message. It's really cool You meet a lot of people so that's tonight But we need to be there at 315 to start setting up and all that stuff So yeah, we're gonna be out of like chapel and class by 11 So I'm gonna come home shower Get ready Good morning, everyone. I'm out of Pilates.  So I'm so kind of like what for my shower But it is currently 8 40 We don't even get into our space until now that I'm trying to finish up editing a video for tonight For her night not for like my channel or anything posted a podcast posted a YouTube video all before 7 a.m It's really incredible We've just been drinking water trying to get this video like done done I thought it was done, but we decided to add more edits to it Which I really like don't have time for some kind of not like stress when I'm like, okay, let's get this done, you know and Yeah, I'm listening to this has been a big week of Dax Shepard armchair expert and listening to that So it's Monica Lewinsky. It's really good 8 37. I'm finishing up stuff on my laptop at 9 I'll go in we have travel at 9 30. We're out at 11. I'll go home shower get ready I have some calls finish up some stuff that are really need done and then I'm heading back to Vancroft Floor her night should be really exciting if you guys live in LA, obviously this is too late But you guys should come one to do I to to her night. It's the best thing ever. All right guys. I'm out of class It was a great chapel. I just got a peppermint cold brew as always and then a breakfast sandwich because I'm just so Hungry and I'm so tired and I'm treating myself because it's her night So very exciting day people Coco is oh my gosh. You're so cute. You've been home by yourself for 30 minutes. I know this So why are you acting like this? Huh? Oh my gosh. She's just so hyper. She gets haircuts and then she has like So much energy for the next week. It's so odd. We have cocoa now So I'm home. I haven't like gone running or anything today But I am gonna shower and like self tan a little bit and stuff get ready for her night because everyone tries a little bit Harder, I have no idea what I'm wearing.  So I'm trying to get everything done And it's gonna be okay All right guys, I just unboxed even more stuff for my princess Polly hole. This bag also is so cool I'm gonna wear it so much at a self tan. So that's why I don't have the straps of my OZON, but Love this just went through my glossier products are received earlier this week I'm actually doing a video with them in the like very near future and as you guys know This is one of my all-time all-time all-time favorite products I wear it every day and I actually just ran out of it like this morning I was like squeezing the last bit of it and I have a new one which is very exciting So I'm gonna go put this in my bag because I wear this literally 24-7. All right So I picked up my outfit for tonight. It is this black bodysuit from princess Polly My Levi's a fun little sparkly belt a pink coat. It's very like cute her and I I'm gonna wear these black Booties with it and then like before I'm gonna wear sweats for a load in Because we're a mobile church. We don't like have a we don't own a building or anything So we have to like load in and load out every single time we have an event So yeah, that is what I'm wearing. I was gonna wear a dress But I just couldn't find one that I loved and this is just comfortable. And so it's what I'm going with All right, I'm ready to go zoomed in. Um load in for the event tonight This is what I'm wearing. I have my new princess Polly bag Full of my stuff that I'm wearing for tonight. I haven't taken that off It looks like I'm going for a sleepover basically. This is the perfect sleepover bag though actually not that I really do that I honestly could not tell you. Well, actually, I can't sleep over anyone's house because I have cocoa I was just thinking if I never do that, but then I remembered that is why so yeah I love this bag that tagging you off. I was watching Chris Cummins video.  I just dried my hair I was gonna curl it, but I just don't feel like it right now. So Whatever happens happens.  So I'll see you guys tomorrow. Good morning everyone. It's Friday morning I wasn't here to Pilates this morning, but it wasn't I was gonna be way too rushed to get to my Recording, so I'm taking today off and it's fine. Um, but her night was great Now it's the next day. I am I don't know why I said I changed. I can't talk This is what I'm wearing. I'm wearing this little Shirt that I got from Princess Polly from it's actually the right good priest though. I'll link it down below It's so cute and I lost my Missouri necklace that I wear every day. So that's not good I'm sure it's somewhere in my house, but it's really bothering me Another pair of my favorite Levi's I need to get more I have to but like these are just the best jeans But they're a little bit big on me right now So I need to wash them, but then I have my Nike Air Force one and then to make the outfit more fun Well, I switched my bags to this one and then I have this cute little coat on because it's actually colder out So that's very exciting. All right guys. Good morning Officially because the guys I think I've gotten like three or four or five of these this week I'm with Quintana. He got a vanilla sweet cream cold brew and I got the peppermint one And then I got a breakfast sandwich. You know, oh my gosh, they normally have the holiday bags um, haha, oh Good for you. I got a breakfast sandwich because I just have no time to eat, but we're heading off I've got the studio Going to some of the video. Have you been to John of Innes? Yeah Whoo All right guys, so I went to the studio I forgot my vlog camera, but I recorded it with Liv Perez It was a really great episode. I did some interest in ads and then I shot some stuff for IGTV for a deer media It's now noon Quintana are going on a cute lunch date because apparently Umami my favorite burger place to ever exist the truffle burger is I can't oh American girl I like cannot even explain How amazing it is apparently they're giving free burgers all day So I feel like that has to be some sort of scam, but apparently it isn't so We're going also I haven't been to the grove yet and there's lights and everything up already So we're gonna be doing that is a bit. Oh my gosh with the line. I figured that's okay. We're not waiting in that line But it's so good What? Okay, well, you know what we can eat somewhere else, but it's so good That's so annoying. Oh my gosh cute hoodie. I didn't even realize you're wearing it Honestly and not even just because you're my girlfriend. It's probably the softest hoodie I own You're hurting here first folks folks, so that's so weird Yeah, don't do valet cuz we don't need to So um Yeah, I like my outfit today, too And we're gonna just walk around a little bit. Maybe Dom's working. Maybe we can say hi to some friends. We'll see Wow guys the tree Wow, I think they're lighting it. Oh, yeah Sunday 17 Wow, it's so beautiful playing Christmas music There's really nothing that makes you happier. I am it's true Christmas basically so we went into on cuz I want you on I know I know guys So beautiful Wow, I love that We ended up a trick or not your friend. She's great back dream. We do love chick-fil-a We do have chick-fil-a comment down below if you guys are a white bread or a brown bread person Obviously, we're brown bread people because that's the right way to be we have this beautiful Christmas view Sitting on the patio the balcony out here. So nice. Love the hoodie Quentin. You look so great in handsome We both got the salmon at lunch special surprise surprise literally all we eat a salmon Another view of the same thing What's your favorite cheesecake though? Normal the Oreo cheesecake here. That's good too. That's like probably the only flavor I get my favorite in the whole world Now we're going off Guys this is four at the Grove the new ones about to be two stories. That's so amazing. How is top shop still there? I'm so confused There we go. We're moving. Wow That's our anthropology is to be RIP missed that store American girl Quick um if you were trapped in an elevator guys, I'll be the first one you would call Yeah, I don't ask Quentin to vlog. He just holds on camera for me insist on it in the box Okay, there's me. No, you can't just Gonna be careful vlogging is serious business you can be in the shot, you know, oh wait, how do I do this? Yeah It goes black sometimes. No, I'm not no.  No, it's like pressure's on oh See I'm learning from the best Um, so really well that lady give us the nastiest look she's from Texas Southern hospitality Okay, we're leaving the grove. I had to drag Because he's really into a skincare I am so And we've got really good fragrances there for guys The keys we got a running joke That I always have the keys, but then I always ask her She always asked I'm always like do the keys. All right. Oh, I have the keys and I wish though. She does what I do But I actually have them this time you know So we're leaving We have just been taking photos Outside also.  This is the first time. This is like the coolest shirt. I think it's yours. I agree, but I It's really unfortunate. We're gonna go home Desafortunadamente Thank you Spanish word of the day people have been loving your dad jokes in the vlogs lately Really? Yeah, I know shock my big pun guy huge pun guy That's right All right guys that this has been I feel like a very very long week. Look at how cute she is. Oh my gosh Here's Quentin. Here's Coco. We love Coco the cutie the other day Quentin was here without me and I you oh my gosh. I just want this lighting me Let me see if I can fix it to tell this great story So the other day what was that we're watching us now the other day I was on my way home and Quentin was already here I'm around the phone and he was with Coco and then I heard him go cutie to Coco I was like, did you just call Coco a cutie? And he's like no So everyone if you made it to the end of this vlog comment Coco the cutie. Hope you guys enjoyed I feel like this is a very big one because I started vlogging a little with my phone Which I feel like you get better footage that way. Let me know what you guys think subscribe if you guys haven't already Thank you for $370,000.  Bye