Introduction to Modern Analysis of PDEs

               (based on the course taught by Anna Kostianko at Imperial College London)  

      Introduction

          Lecture 1:       capture         slides    Anna’s notes  1

      Part I: Distributions

                  Lecture 2:       capture         slides       

                  Lecture 3:       capture         slides

                  Lecture 4:       capture         slides

                  Anna’s notes   1  2  3  4  5  6

                  Problems for Part I:  pdf   Solutions: pdf

      Part II: Sobolev spaces and embedding theorems

                  Lecture 5:      capture          slides

                  Lecture 6:      capture          slides

                  Lecture 7:      capture          slides

                  Anna’s notes  8  9  10  11  12

                  Problems for Part II:   pdf    Solutions:  pdf

      Part III: Linear Elliptic Equations and Spectral Theory

                   Lecture 8:      capture          slides

                   Lecture 9:      capture          slides

                   Lecture 10:    capture          slides

                   Lecture 11:    capture          slides

                   Lecture 12:    capture          slides

                   Anna’s notes  13  14-15 16  17 18 19 20-21 22 23

                   Problems for Part III:  pdf   Solutions: pdf

      Part IV: Linear evolution equations

                   Lecture 13:    capture                          slides

                   Lecture 14:    capture   capture         slides 

                   Anna’s notes 24-25 26-27

                   Problems for Part IV-V:  pdf   Solutions: pdf

      Part V: Semilinear equations                            

                   Lecture 15:    capture          slides

                   Anna’s notes 28-29

      MOCK EXAM   pdf    with SOLUTIONS    pdf

      Unassessed Coursework pdf   with solutions pdf