18.152 - Course Notes (Spring 2018)

 

 

 

Date Topic+ Link to course notes
2-6-18 Introduction to PDEs
2-8-18 Introduction to the heat equation
2-13-18 The heat equation: Uniqueness
2-15-18 The heat equation: Weak maximum principle and introduction to the fundamental solution
2-20-18 No class (Monday class schedule)
2-22-18 The heat equation: Fundamental solution and the global Cauchy problem
2-27-18 Laplace's and Poisson's equations
3-1-18 Poisson's equation: Fundamental solution
3-6-18 Poisson's equation: Green functions
3-8-18 Poisson's equation: Poisson's formula, Harnack's inequality, and Liouville's theorem
3-13-18 Introduction to the wave equation
3-15-18 The wave equation: The method of spherical means
3-20-18 The wave equation: Kirchhoff's formula and Minkowskian geometry
3-22-18 Midterm Exam
4-3-18 The wave equation: Geometric energy estimates
4-5-18 The wave equation: Geometric energy estimates (continued)
4-10-18 Classification of second order equations
4-12-18 Introduction to the Fourier transform
4-19-18 Introduction to the Fourier transform (continued)
4-24-18 Fourier inversion and Plancherel's theorem
4-26-18 Introduction to Schrödinger's equation
5-1-18 Introduction to Schrödinger's equation (continued)
5-3-18 Introduction to Lagrangian field theories
5-8-18 Introduction to Lagrangian field theories (continued)
5-10-18 Introduction to Lagrangian field theories (continued)
5-15-18 Transport equations and Burger's equation
5-17-18 Transport equations and Burger's equation (continued)