hello guys so I am going to start a new series on discussing some sort of theoretical perspective of partial differential equations and I believe that you won't be able to find such a course available on YouTube mostly because there are so many courses and they discuss partial differential equations from some sort of Applied point of view where let's say you take different pdes and solve them by using different methods but you won't be able to find such a course that I am going to discuss Maybe because I have never found so this is the course on theory of partial differential equations and in this very first video which is going to be maybe at most five minutes in length I am going to discuss only the syllabus or the content of the course that we are going to cover about then I'll try to keep the lectures that I am going to record Maybe two or three lectures per week or more than that and you can just wash them in your free time and you can just schedule anything and you can watch the lectures and after maybe four or five lectures I'll be letting you know that okay I'm going to share some sort of homework assignments with you and you just need to solve them and tell me in the comments said okay you have solved then I can I can just give you some sort of my communication device so that you just send me your homework solutions and I can check those and send you the solutions back and I've also shared the link of my guitar page down in the description where you can find the syllabus and and the lectures that we are going to do day by day are two three lectures in a week so the prerequisites for this course are you can see the name of the courses theory of partial differential equations and the prerequisites are Advanced calculus Advanced mathematical analysis function analysis and major Theory but I believe that the like more rigorous Foundation of these courses is not required because this is a course on theory of partial differential equations if you know basic real analysis that is I think there's going to be enough for us I'll be discussing functional analysis and major Theory maybe in first couple of lectures the main big theorems in these courses that we'll be applying to study theory of partial differential equations so here is the course content the main thing is we'll review function analysis and measure Theory like Bannock and Hilbert spaces dual spaces reuse representation theorem X Milgram weekend weak star convergence the bag measure and integral so these are the main chunks from function analysis and major theory that we will be going to revise and then we'll be applying these things in the study of partial differential equations we'll be doing some function spaces mostly LP spaces we'll discuss convolution which are really important modifiers and some useful function inequalities in in analysis of pdes so the next part after this for the course will be Sublime spaces and the weak derivatives and obviously their calculus the calculus of weak derivatives and the point gray inequality the famous inequality when we study partial differential equations and some of the embedding terms and several spaces after this the main part of this course like you have done the basic Theory major Theory function analysis and some functions passive and so will always passes now you can now you can talk about linear elliptic equations you can talk about the existence and uniqueness of their Solutions you can talk about the regularity and also elliptic regularity which is very famous when you are talking about elliptic equations and one of the example is LaPlace equation we can talk about organ function expansion LaPlace in person equations will be our main examples that we'll be discussing after this we'll discuss a bit about Fourier series and glare can message and this method will help us to solve to to make sense of some sort of weak Solutions of linear probability equations and for this the main example is the heat equation so like we will do some sort of existence and uniqueness for the theory of heat equation from the perspective of glarkin method and obviously we will be discussing the space of distributions before these all the things we'll be discussing some sort of fundamental Solutions we'll be discussing Fourier transform and L2 Hilbert spaces and these other things so this is like this is this is the main main content of the course of theory of partial differential equations if you want to do something advanced then then the next thing is like the theory of existence and uniqueness of the solutions are never historic's equations in 2D and 3D obviously the existence in uniqueness is a problem in 3D it's still an open problem in Millennium problem but will make sense in 2D and we'll just ify that why it's not that much simple to discuss the case in 3D and recently I have been working on a paper from Ray is the famous mathematician from 1930s he wrote a paper on every Stokes equations and it is one of the most celebrated paper in this all set up I I have been recently studying this paper and at the end of this I will be discussing this paper this is actually in in French but like there are English translations of this paper as well but I'll be discussing note the paper exactly but some sort of modern version of that paper that is written by different people and that is written by one of the person at our University and I'll be discussing that paper from the very beginning so if you if you don't need to go for that that's okay but if some people are interested you can also go for this thing so the the main part of course is the first first few bullets that I showed you you're not supposed to go for never strokes but if you are interested you can go this would be the lighter version of Never Stokes but in this paper there would be some sort of in-depth version of these all the things the textbooks that I'm going to refer you are these the first one is partial differential equations by Evans this is one of the most famous book and you can see this is going to be the front page and it is easily available in market and you can simply download it and print the pages that you need to read print the chapters depends even you can buy it as well from the market from Amazon from eBay from any other any other place which you find suitable and easy for you the next book that I like the most is Introduction to partial differential equations by David bossvik this is really a nice book if you want to study uh like partial differential equations from some sort of applied and pure both perspectives this is really nice book and I can show you the front page is this enter David both speak introduction to partial differential equations in the next book I'm in this infinite dimensional dynamical systems and and this is by GEM C Roberson this is a really nice book and it simply contains the very few seven or eight chapters only contains this theory of partial differential equations in existence and uniqueness there is gallarkin method like this is going to be the main reference for our course this is really simple and nicely written if you want to just follow my lectures and read this book and do the exercises I am going to assign you then this is going to be a great thing to follow through so see you in the very first lecture in in the very first lecture I'll be starting to discuss function analysis in the major results in the very second lecture I will be discussing major theory in the famous results in major Theory then we'll be digging deep into what we need to discuss in partial differential equations so till then goodbye and see you