18.152 - Course Notes (Spring 2017)

 

 

 

Date Topic+ Link to course notes
2-7-17 Introduction to PDEs
2-9-17 Snow day
2-14-17 Introduction to the heat equation
2-16-17 The heat equation: Uniqueness
2-23-17 The heat equation: Weak maximum principle and introduction to the fundamental solution
2-28-17 The heat equation: Fundamental solution and the global Cauchy problem
3-2-17 Laplace's and Poisson's equations
3-7-17 Poisson's equation: Fundamental solution
3-9-17 Poisson's equation: Green functions
3-14-17 Poisson's equation: Poisson's formula, Harnack's inequality, and Liouville's theorem
3-16-17 Introduction to the wave equation
3-21-17 The wave equation: The method of spherical means
3-23-17 The wave equation: Kirchhoff's formula and Minkowskian geometry
4-4-17 The wave equation: Geometric energy estimates
4-6-17 Midterm Exam
4-11-17 The wave equation: Geometric energy estimates (continued)
4-13-17 Classification of second order equations
4-20-17 Introduction to the Fourier transform
4-25-17 Introduction to the Fourier transform (continued)
4-27-17 Fourier inversion and Plancherel's theorem
5-2-17 Introduction to Schrödinger's equation
5-4-17 Introduction to Schrödinger's equation (continued)
5-9-17 Introduction to Lagrangian field theories
5-11-17 Introduction to Lagrangian field theories (continued)
5-16-17 Introduction to Lagrangian field theories (continued)
5-18-17 Transport equations and Burger's equation