Below is a tentative course schedule. I will try to stick to this plan as much as possible. If I start deviating too much from the intended schedule, I will make updates to this page.
| Class | Subjects | Reference |
|---|---|---|
| 9/26 | Introduction; Definitions; Classification of equations in terms of degrees of nonlinearity. | Strauss: Sec. 1.1-1.5; Evans: Chap. 1 |
| 10/1 | First-Order Equations; Method of Characteristics. | Strauss: Sec. 1.2; Evans: Sec. 3.2 |
| 10/3 | Quasilinear and Fully Nonlinear Equations. | Evans: Sec. 3.2 |
| 10/8 | Conservation Laws: Weak Solutions, Rankine-Hugoniot Jump Condition, Shocks. | Strauss: Sec. 14.1; Evans: Sec. 3.4 |
| 10/10 | Conservation Laws: Rarefaction Waves, Entropy Conditions, Riemann Problem. | Strauss: Sec. 14.1; Evans: Sec. 3.4 |
| 10/15 | Long-Time Asymptotics; Oleinik Entropy Condition. | Evans: Sec. 3.4.5 |
| 10/17 | Classification of Second-Order Equations. | Strauss: Sec. 1.6 |
| 10/22 | Wave Equation in 1-D; d'Alembert's Formula; Energy Methods. | Strauss: Sec. 2.1-2.2; Evans: Sec. 2.4.1.a |
| 10/24 | Domain of Dependence; Inhomogeneous Equation. | Strauss: Sec. 2.2, 3.4; Evans: Sec. 2.4.3 | 10/29 | Duhamel's Principle; Wave Equation on the Half-Line; Wave Equation on an Interval: Reflection of Waves. | Strauss: Sec. 3.2, 3.4; Evans: Sec. 2.4.1.a |
| 10/31 | Separation of Variables; Eigenvalue Problems. | Strauss: Chapter 4 |
| 11/5 | Midterm. | |
| 11/7 | Orthogonality and Symmetric Boundary Conditions; Fourier Series. | Strauss: Sec. 5.1-5.3 |
| 11/12 | Convergence of Fourier Series. | Strauss: Sec. 5.4-5.5 |
| 11/14 | Inhomogeneous Wave Equation on an Interval; Inhomogeneous Boundary Data. | Strauss: Sec. 5.6 |
| 11/19 | Wave Equation in Higher Dimensions: Kirchoff's Formula, Hadamard's Method of Descent. | Strauss: Sec. 9.2; Evans: Sec. 2.4.1.b-2.4.1.e |
| 11/21 | Wave Equation in Higher Dimensions: Huygen's Principle; Wave Equation with a Source, Wave Equation on a Bounded Domain. | Strauss: Sec. 9.2, 10.1; Evans: Sec. 2.4.1.b-2.4.1.e, 2.4.2 |
| 11/26 | Hyperbolic Systems: Definitions, Examples. | Evans: Sec. 7.3 |
| 12/3 | Domain of Dependence for Symmetric Hyperbolic Systems. | Evans: Sec. 7.3 |
| 12/5 | Catch-up/Review. |