18.152 - Course Notes (Fall 2011)
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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 SchrÃ¶dinger's equation
11-22-11
Introduction to SchrÃ¶dinger'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