# MATH400-101 : Applied Partial Differential Equations (First term 2019-2020)

### Lecture I: Monday 9:00am--10:00am, LSK-460.

### Lecture II: Wednesday 9:00am--10:00am, LSK-460.

### Lecture III: Friday 9:00am--10:00am, LSK-460.

### Office Hours: Every Monday, Wednesday, 4:30pm-5:30pm, Tuesday, Thursday, 1-2pm, LSK 303B.

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# Lecture Notes For MATH400-101

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# Updates For MATH 400-101

### First class: Sept 4, 2019

### Sept 4: Introduction to PDEs; 1st order linear PDE; introduction to characteristic curves and initial data curve.

### Sept 6: Characteristic curves for Case 1 $ a(x,y) u_x+ b (x, y) u_y=0$. Examples. Domain of Existence.

### Sept 9: Example 6 of Lecture Note 1. Method of Characteristics for Case 2 $ a(x, y)+ b(x, y) u_y= d(x, y, u)$. Example 8, 9, 11 of Lecture Note 1. Please replace Example 10 in Lecture Note 1 Example 10 (Lecture 1)

### Sept 11: Example 8, 10 of Lecture Notes One. Start on General Solutions of Case 2.

### Sept 13:General solution for Case 2. Finished Lecture Note 1. Start on Lecture Note 2.

### Sept 16: Lecture Note 1. Quasilinear First order PDEs. Method of Characteristic Curves. Break-up time.

### Lecture Note 2: Expansion fans, shock curves. Rankine-Hugoniot condition.

# Announcements For MATH 400-101

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