18.152 - Course Notes (Fall 2011)

 

 

 

DATE TOPIC + LINK TO COURSE NOTES
9-08-11 Introduction to PDEs
9-13-11 Introduction to the heat equation
9-15-11 The heat equation: Uniqueness
9-20-11 The heat equation: Weak maximum principle and introduction to the fundamental solution
9-22-11 The heat equation: Fundamental solution and the global Cauchy problem
9-27-11 Laplace's and Poisson's equations
9-29-11 Poisson's equation: Fundamental solution
10-04-11 Poisson's equation: Green functions
10-06-11 Poisson's equation: Poisson's formula, Harnack's inequality, and Liouville's theorem
10-13-11 Introduction to the wave equation
10-18-11 The wave equation: The method of spherical means
10-20-11 The wave equation: Kirchhoff's formula and Minkowskian geometry
10-25-11 The wave equation: Geometric energy estimates
10-27-11 Midterm Exam
11-01-11 The wave equation: Geometric energy estimates (continued)
11-03-11 Classification of second order equations
11-08-11 Introduction to the Fourier transform
11-10-11 Introduction to the Fourier transform (continued)
11-15-11 Fourier inversion and Plancherel's theorem
11-17-11 Introduction to Schrödinger's equation
11-22-11 Introduction to Schrödinger's equation (continued)
11-29-11 Introduction to Lagrangian field theories
12-01-11 Introduction to Lagrangian field theories (continued)
12-06-11 Introduction to Lagrangian field theories (continued)
12-08-11 Transport equations and Burger's equation