Calendar

SES # TOPICS KEY DATES
L1 Introduction to PDEs  
L2 Introduction to the heat equation  
L3 The heat equation: Uniqueness Problem Set 1 due
L4 The heat equation: Weak maximum principle and introduction to the fundamental solution  
L5 The heat equation: Fundamental solution and the global Cauchy problem Problem Set 2 due
L6 Laplace’s and Poisson’s equations  
L7 Poisson’s equation: Fundamental solution Problem Set 3 due
L8 Poisson’s equation: Green functions  
L9 Poisson’s equation: Poisson’s formula, Harnack’s inequality, and Liouville’s theorem Problem Set 4 due
L10 Introduction to the wave equation Problem Set 5 due
L11 The wave equation: The method of spherical means  
L12 The wave equation: Kirchhoff’s formula and Minkowskian geometry Problem Set 6 due
L13 The wave equation: Geometric energy estimates  
E1 Midterm Exam  
L14 The wave equation: Geometric energy estimates (cont.)  
L15 Classification of second order equations Problem Set 7 due
L16 Introduction to the Fourier transform  
L17 Introduction to the Fourier transform (cont.) Problem Set 8 due
L18 Fourier inversion and Plancherel’s theorem  
L19 Introduction to Schrödinger’s equation Problem Set 9 due
L20 Introduction to Schrödinger’s equation (cont.)  
L21 Introduction to Lagrangian field theories Optional (Bonus) Problem due
L22 Introduction to Lagrangian field theories (cont.) Problem Set 10 due
L23 Introduction to Lagrangian field theories (cont.)  
L24 Transport equations and Burger’s equation Problem Set 11 due
E2 Final Exam  

Course Info

Learning Resource Types

assignment Problem Sets
grading Exams with Solutions
notes Lecture Notes