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 
Calendar
Instructor:  
Course Number: 

Departments:  
As Taught In:  Fall 2011 
Level: 
Undergraduate

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assignment
Problem Sets
grading
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notes
Lecture Notes