Textbook abbreviations E = Evans' PDE HL = Han and Lin's Lecture Notes on PDE GT = Gilbarg and Trudinger's Second Order Elliptic PDE Ld = Landis' Second order equations of elliptic and parabolic type J = Jost's Partial differential equations

Date Topics Sections Event Week 1                 09-23 Introduction to PDEs-- problems and methods E Ch1; Week 2 09-26 Basic Linear PDEs I E Ch2 09-28 Basic Linear PDEs II E Ch2 09-30 Basic Linear PDEs III E Ch2   Week 3 10-03 Basic Linear PDEs-including the wave equation IV E Ch2 10-05 Basic Linear PDEs-including the wave equation V E Ch2 10-07 Basic Linear PDEs-including the wave equation VI E Ch2 Week 4 10-10 Nonlinear first order PDEs-including Hamilton Jacobi equation I E Ch3   10-12 Nonlinear first order PDEs-including Hamilton Jacobi equation II E Ch3 10-14 Nonlinear first order PDEs-including Hamilton Jacobi equation III E Ch3   Week 5 10-17 Nonlinear first order PDEs-including Hamilton Jacobi equation IV E Ch3 Homework 1 is due 10-19 Nonlinear first order PDEs-including Hamilton Jacobi equation IV E Ch3 10-21 Make-up/Catch-up Week 6 10-24 Sobolev Spaces I E Ch5   10-26 Sobolev Spaces II E Ch5   10-28 Sobolev Spaces III E Ch5 Week 7 10-31 Sobolev Spaces IV E Ch5 11-02 Sobolev Spaces V E Ch5   11-04 Sobolev Spaces VI E Ch5 Week 8 11-07 Elliptic equations--weak solution method I E Ch6 Homework 2 is due 11-09 Elliptic equations II E, Ch 6 11-11 Holiday Holiday   Week 9 11-14 Elliptic equations- III E Ch6   11--16 Elliptic equations IV E Ch6 11-18 Elliptic equations V E Ch 6 Week 10 11-21 Eigenvalues-I Notes-I   11-23 Eigenvalues-II Notes 11-25 Holidays Holidays   Week 11 11-28 Parabolic equations-I E Ch 7   11-30 Parabolic equations-II E Ch7 Homework 3 is due 12-02 Parabolic equations III E Ch7

Textbook abbreviations

Date Topics Sections Event Week 1 01-09 Maximum Principle I E Ch6, HL Ch2   01-11 Maximum Principle II E Ch6, HL Ch2   01-13 Maximum and Gradient estimates for solutions E Ch 6, HL Ch2 hand-outs Week 2 01-16 Happy Holiday Happy Holiday Happy Holiday 01-18 Harnack inequality and local gradient estimate for nonlinear equations HL Ch2 01-20 Eigenvalues for symmetric elliptic operators HL Ch2 Problem 12 of 6.6 is due Week 3 01-23 A digression to functional analysis E Ch6 01-25 The first eigenvalue and eigenfunction for symmetry operator E Ch6 01-27 The first eigenvalue for the nonsymmetric operator E Ch6 Week 4 01-30 Eigenvalue and parabolic equation E Ch6, 7 Problem 13 of Section 6.6 is due 02-01 Parabolic equation-weak solution-Galerkin method I E Ch7 02-03 Parabolic equation-weak solution-Galerkin method II E Ch3 Week 5 02-06 Parabolic equation-Maximum principle E Ch3 Problem 2 and 3 of Section 7.5 is due 02-08 Existence of the heat potential I Ld Ch3 02-10 Weyl's asymptotics on eigenvalues I Notes by Simon Week 6 02-13 Weyl's asymptotics on eigenvalues II   Problem 6 of Section 6.6,Problem 6 of Section 7.5 are due 02-15 Hyperbolic equations-Galerkin method E Ch7 02-17 Hyperbolic system E Ch7   Week 7 02-20 Happy Holiday Happy Holiday Happy Holiday 02-22 Introduction to nonlinear PDEs-I E Ch9   02-24 Introduction to nonlinear PDEs-II E Ch9 Problem 8 of Section 6.6, problem 10 of Section 7.5 Week 8 02-27 Introduction to nonlinear PDEs-III E Ch9 02-29 Introduction to nonlinear PDEs-VI E Ch9 03-02 Introduction to nonlinear PDEs-V E Ch9   Week 9 03-05 Maximum principle for weak solutions-De Gorgi's trick HL Ch4   03-07 Harnack estimate II -for weak solutions HL Ch 4 03-09 Alexandrov maximum principle I HL Ch2 Week 10 03-12 Alexandrov maximum Principle II HL Ch2   03-14 Introduction to Ricci flow I-the short time existence Notes 03-16 Introduction to Ricci flow II-the short time existence Notes