Course Schedule |
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| Date | Day | Ch | Topics | |
| Jan | 20 | W | 7 | First Order PDEs - Intro |
| 22 | F | 7 | Quasilinear PDEs - Method of Characteristics | |
| 26 | M | 7 | Conservation Law, Advection and Burgers Equation | |
| 28 | W | 7 | Shocks | |
| 30 | F | 7 | Rarefactions, Traffic Flow | |
| Feb | 1 | M | 7 | Nonlinear First Order Equations |
| 3 | W | 7 | More Examples | |
| 5 | F | 8 |
Nonhomogeneous Equations and Green's Functions |
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| 8 | M | 8 | Initial Value Green's Function/Variation of Parameters | |
| 10 | W | 8 | Boundary Value Green's Function | |
| 12 | F | 8 | ODE Green's Functions - Properties | |
| 15 | M | 8 | Differential Equation and Dirac Delta Function | |
| 17 | W | 8 | ODE Green's Functions - Series Representation | |
| 19 | F | 8 | Green's Functions for PDEs | |
| 22 | M | 8 | Nonhomogeneous Heat Equation | |
| 24 | W | 8 | Green's Function -Heat Equation | |
| 26 | F | 8 | Poisson Equation/Method of Images | |
| Mar | 1 | M | 8 | Eigenfunction Expansions |
| 3 | W | Midterm | ||
| 5 | F | 9 | Complex Numbers and Functions | |
| 8 | M | 9 | Derivatives/Harmonic Functions | |
| 10 | W | 9 | Complex Integration | |
| 12 | F | 9 | Cauchy's Theorem/Analytic Functions | |
| 15 | M | 9 | Cauchy Integral Formula/Laurent Series | |
| 17 | W | 9 | Singularities/Residue Theorem | |
| 19 | F | 9 | Real-valued Integrals/Cauchy Principal Value | |
| 22 | M | 9 | Real-valued Integrals/Jordan's Lemma | |
| 24 | W | 9 | Multivalued Integrands/2D Fluid Flow | |
| 26 | F | 9 | Conformal Mapping/Bilinear Transformations | |
| 29 | M | 9/10 | Laplace's Equation - Complex Domain/Integral Transform | |
| 31 | W | 10 | Fourier Transform - Derivation | |
| Apr | 2 | F | No Class | |
| 5 | M | 10 | Fourier Transform Properties/Gaussians and the Heat Kernel | |
| 7 | W | 10 | Parseval's Theorem/Laplace's Equation Semi-infinite Domain | |
| 9 | F | 10 | Laplace Transforms | |
| 12 | M | 10 | Laplace Transforms and PDEs | |
| 14 | W | Numerical Solution of Advection Equation | ||
| 16 | F | Truncation Error and Stability | ||
| 19 | M | Other Methods - Iterative/Spectral/Finite Element | ||
| 21 | W | Dispersive Waves, Asymptotics | ||
| 23 | F | Nonlinear PDEs - KdV, Burgers | ||
| 26 | M | Kinks and Breathers - NLS and sine-Gordon | ||
| 28 | W | Reaction-Diffusion - Pattern Formation | ||
| 29 | R | Reading Day | ||
| May | 5 | W | Final 8:00-11:00 AM |