| Coursework (due on November 1st, 23:59pm) |
 Coursework Solutions |
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| Week 1: Basic concepts of PDE, order, linearity and homogeneity |
Week 1 notes |
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Problem set 1 |
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Review of some ODE techniques |
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Selected solutions to Problem set 1 |
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Extra selected solutions to Problem set 1 |
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| Week 2: Solving first order PDEs using change of coordinates and characteristics |
Week 2 notes |
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Problem set 2 |
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Selected solutions to Problem set 2 |
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| Week 3: Classification of second order PDEs and D'Alembert's formula for wave equations on the real line |
Week 3 notes |
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Problem set 3 |
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Selected solutions to Problem set 3 |
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Extra selected solutions to problem set 3 |
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| Week 4: Energy for wave equations, wave equations on the half line |
Week 4 notes |
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Problem set 4 |
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Selected solutions to Problem set 4 |
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| Week 5: Separation of variables and wave equations on the intervals |
Week 5 notes |
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Problem set 5 |
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Problem set 5 selected solutions |
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| Week 6: Duhamel's principle and inhomogenous wave equations |
Week 6 notes |
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Problem set 6 |
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Problem set 6 selected solutions |
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| Week 8: Harmonic functions and Laplace equations on symmetric domains |
Week 8 notes |
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Problem set 7 |
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Selected solutions to Problem set 7 |
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| Week 9: Properties of harmonic functions and heat equations on the intervals |
Week 9 notes |
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Problem set 8 |
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Selected solutions to Problem set 8 |
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| Week 10: Heat equation on the real line and the heat kernel |
Week 10 notes |
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Problem set 9 |
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Problem set 9 selected solutions |
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| Week 11: Heat equations on the half line and maximum principles |
Week 11 notes |
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Problem set 10 |
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Selected solutions to Problem set 10 |
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| Week 12: Review |
Key review checkpoints |
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| Sample past exam papers |
2022-2023 exam |
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2022-2023 exam solutions |
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2023-2024 exam |
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2023-2024 exam solutions |
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