# MATH400-201 : Applied Partial Differential Equations (2nd term 2013/2014)

### Lecture I: Tuesday 9:30am--11:00am, Math Annex 1100.

### Lecture II: Thursday 9:30am--11:00am, Math Annex 1100.

### Office Hours: Every Monday, Wednesday, Friday, 4pm-5pm, LSK 303D.

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# Downloads For MATH400

# Updates For MATH 400

### Jan. 7: Method of Characteristics. Four Examples.

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### Jan. 9: Method of Characteristics. More Examples including blow-ups. Method of Change of Variables.

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### Jan. 14: General solutions using method of change of variables. Example in which the data curve coincides precisely with characteristics. Condition on initial condition. Up to page 1.23 of lecture note one.

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### Jan. 16: Quasilinear 1st Order PDE. Traffic Flow Model. Characteristics Meet. Breaking Time. up to page 2.9 of lecture note two.

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### Jan. 21: Shock. Rankine-Hugoniot Condition. Examples of Shock curves. Finished Lecture Note Two.

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### Jan. 23: Fully nonlinear first order PDEs. Eikonal Equation. Finished Lecture Note Three.

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### Jan. 28: Eikonal Equation. Derivation of Wave Equation and Diffusion Equation. Finished up to 1.3 of Lecture Note Four.

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### Jan. 30: Initial and Boundary Conditions. Types of Second Order PDE. Finished up to 1.6 of Lecture Note Four.

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### Feb. 4: Classification of 2nd order linear PDEs using the change of variables. General solutions of wave equation, d'Alembert's formula. Three examples

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### Feb. 6: Principle of Causality. Domain of Influence/Dependence. Wave Equation with Sources. Well-posedness of Wave Equation.

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### Feb. 11, Feb. 13: Reflection of Waves. Solution Formula for Diffusion Equation. Up to lecture note 7.

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### Feb. 25: Diffusion with source. well-posedness. Reflection. Up to Lecture note 8.

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### March 4: Midterm

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### March 6: Method of Separation of Variables. Cases of negative eigenvalues. Lecture Note 9.

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### March 11: Lecture Note 9. Periodic Boundary Conditions.

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### March 13: Lecture Note 10. Finished up to Example 2.

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### March 18: Lecture 10 and Lecture 11: up to the method of separation of variables to inhomogeneous heat equation.

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### March 20: Lecture 11 and the beginning of Lecture 12 (uniqueness).

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### March 25: Solving Laplace equation in rectangles and cubes. Lecture 12.

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### March 27: Laplace operator in polar coordinate. Solve Poisson equation in a disk. Poisson formula. Lecture 13.

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### April 1: Solve Poisson equation in a wedge, an annulus, and exterior of a disk. Maximum Principle.

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### April 3: Laplace with inhomogeneous source. existence and uniqueness in unbounded domains. Heat equation in a disk--introduction of Bessel function.

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### April 8: Bessel function of order zero and Bessel function of order $n$. Finished Lecture Note 14. Have a nice final exam

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### April 23: Final Exam.

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# Announcements For MATH 400

### Office Hours: Every Monday, Wednesday, Friday, 4pm-5pm, LSK 303D. Starting Date: Jan. 8

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### Homework Two has been revised on Jan. 24.

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### Midterm Examination Date: March 4 (Tuesday) in class.

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### Coverage of Midterm Examination: up to Lecture Note 8.

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### Last homework assignment (HW#7) will be handed out on April 8th.

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### There will still be office hours on April 11, April 14 and April 16. Same time and same location.

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### Last Office Hour on Tuesday (April 22). Same time and same location. You can collect your last homework.