18.152 | Fall 2011 | Undergraduate

Introduction to Partial Differential Equations

Lecture Notes

L1 Introduction to PDEs (PDF)
L2 Introduction to the heat equation (PDF)
L3 The heat equation: Uniqueness (PDF)
L4 The heat equation: Weak maximum principle and introduction to the fundamental solution (PDF)
L5 The heat equation: Fundamental solution and the global Cauchy problem (PDF)
L6 Laplace’s and Poisson’s equations (PDF)
L7 Poisson’s equation: Fundamental solution (PDF)
L8 Poisson’s equation: Green functions (PDF)
L9 Poisson’s equation: Poisson’s formula, Harnack’s inequality, and Liouville’s theorem (PDF)
L10 Introduction to the wave equation (PDF)
L11 The wave equation: The method of spherical means (PDF)
L12 The wave equation: Kirchhoff’s formula and Minkowskian geometry (PDF)
L13–L14 The wave equation: Geometric energy estimates (PDF)
L15 Classification of second order equations (PDF)
L16–L18 Introduction to the Fourier transform; Fourier inversion and Plancherel’s theorem (PDF)
L19–L20 Introduction to Schrödinger’s equation (PDF)
L21-L23 Introduction to Lagrangian field theories (PDF)
L24 Transport equations and Burger’s equation (PDF)

Course Info

As Taught In
Fall 2011
Learning Resource Types
Problem Sets
Exams with Solutions
Lecture Notes