Lecture Plans
Introduction
- Day 01: Introduction to PDEs (1.1)
- Day 02: PDE modeling (1.2, 1.3)
- Day 03: Review of ODEs, series solutions (Chapter 5 of Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems 10th ed.)
Classification of PDEs
- Day 04: First-order equations (1.2)
- Day 05: Initial and boundary conditions, well-posed problems (1.4, 1.5)
- Day 06: Types of second-order equations (1.6)
Wave Equations
- Day 07: Vibrations of a drum (1.3, 2.1)
- Day 08: Causality and energy (2.2)
- Day 09: Reflections of waves (3.2), waves with a source (3.4)
Diffusion Equations
- Day 10: Diffusion on the whole line (2.3, 2.4)
- Day 11: Diffusion on the half-line (3.1),
- Day 12: Diffusion with a source (3.3)
Boundary Value Problems
- Day 13: Separation of variables, boundary conditions (4.1)
- Day 14: Fourier transforms - orthogonality and completeness (5.1, 5.3, 5.4)
- Day 15: Laplace’s equation, Poisson’s equation (6.1, 6.2, 6.3)
Eigenvalue Problems
- Day 16: Computation of eigenvalues (11.2, 11.3)
- Day 17: Symmetric differential operators (11.4)
- Day 18: Asymptotics of eigenvalues (11.6)
Distributions and Weak Formulation
- Day 19: Weak solutions, FEM (8.5)
- Day 20: Distributions (12.1, 12.2)
- Day 21: Green’s functions (7.1, 7.2, 7.3)
Function Spaces
- Day 22: Hilbert space
- Day 23: Lax-Milgram theorem
- Day 24: Banach space
Abstract Formulation
- Day 25: Second-order elliptic equations
- Day 26: Second-order linear evolution equations
- Day 27: Semigroup theory
Review
- Day 28: Review