Lecture Plans
Livestream lectures: Zoom.
Recorded lectures: available on Canvas.
Introduction
- Day 01 (Sep 14): Introduction to PDEs (1.1)
- Day 02 (Sep 16): PDE modeling (1.2, 1.3)
- Day 03 (Sep 18): 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 (Sep 21): First-order equations (1.2)
- Day 05 (Sep 23): Initial and boundary conditions, well-posed problems (1.4, 1.5)
- Day 06 (Sep 25): Types of second-order equations (1.6)
Wave Equations
- Day 07 (Sep 28): Vibrations of a drum (1.3, 2.1)
- Day 08 (Sep 30): Causality and energy (2.2)
- Day 09 (Oct 02): Reflections of waves (3.2), waves with a source (3.4)
Diffusion Equations
- Day 10 (Oct 05): Diffusion on the whole line (2.3, 2.4)
- Day 11 (Oct 07): Diffusion on the half-line (3.1),
- Day 12 (Oct 09): Diffusion with a source (3.3)
Boundary Value Problems
- Day 13 (Oct 12): Separation of variables, boundary conditions (4.1)
- Day 14 (Oct 14): Fourier transforms - orthogonality and completeness (5.1, 5.3, 5.4)
- Day 15 (Oct 16): Laplace’s equation, Poisson’s equation (6.1, 6.2, 6.3)
Eigenvalue Problems
- Day 16 (Oct 19): Computation of eigenvalues (11.2, 11.3)
- Day 17 (Oct 21): Symmetric differential operators (11.4)
- Day 18 (Oct 23): Asymptotics of eigenvalues (11.6)
Distributions and Weak Formulation
- Day 19 (Oct 26): Weak solutions, FEM (8.5)
- Day 20 (Oct 28): Distributions (12.1, 12.2)
- Day 21 (Oct 30): Green’s functions (7.1, 7.2, 7.3)
Function Spaces
- Day 22 (Nov 02): Hilbert space
- Day 23 (Nov 04): Lax-Milgram theorem
- Day 24 (Nov 06): Banach space
Abstract Formulation
- Day 25 (Nov 09): Second-order elliptic equations
- Day 26 (Nov 11): Second-order linear evolution equations
- Day 27 (Nov 13): Semigroup theory
Review
- Day 28 (Nov 16): Review