# MATH400-201 : Applied Partial Differential Equations (2nd term 2015/2016)

### 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, 4:30pm-5:20pm, LSK 303B.

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# Lecture Notes For MATH400

# Downloads For MATH400

# Updates For MATH 400

### Jan. 4: Method of Characteristics.

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### Jan. 7: Method of Characteristics for linear and quasilinear 1st order PDE.

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### Jan. 12: Method of change of variables to obtain general solutions.

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### Jan. 14: Quasilinear first order PDEs. Expansion Fan.

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### Jan. 19: Expansion Fans and shocks. Traffic flow problems. Lecture Notes 2.

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### Jan. 21: First order fully nonlinear PDE (Lecture 3).

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### Jan. 26: Derivation of Wave and heat Equations. Well-posedness of PDE problems. (Lecture 4).

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### Jan. 28: Classification of 2nd order linear PDE. Change of variables. Lecture 4.

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### Feb: 2. D'Alembert's formula. General solutions for general hyperbolic equations.

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### Feb. 4: Wave equations on quarter plane. Wave equation with discontinuous speed. Wave equation with source. Lecture Note 5.

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### Feb. 9: Wave equations with sources. Wave equation on half line. Lecture note 5.

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### Feb. 11: Wave equation on a bounded domain. Lecture Note 6. Diffusion Equation. Lecture Note 7.

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### Feb. 25: Diffusion Equation with initial and sources. Lecture Note 8 and 9.

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### March 1: Diffusion equation on half space. Lecture Note 8.

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### March 3: Method of Separation of Variables. Lecture Note 9.

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### March 8: Method of Separation of Variables. Lecture Note 9.

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### March 10: Remarks on Lecture Note 9.5. Reduction to Sturm-Liouville EVP. Lecture Note 10.

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### March 15: General S-L Problems. Examples. Lecture Note 11.

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### March 17: General S-L Problems. Finished Lecture Note 11.

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### March 22: Method of Separations to inhomogeneous. Lecture Note 12.

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### March 24: Laplace equation. Uniqueness by energy method. Method of Separation of Variables to rectangles, cubes. Lecture Note 12/13.

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### March 29: Poisson formula. Applications.

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### March 31: Annulus, Exterior Domain, Wedges. Bessel Function.

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### April 5: Bessel functions of order $n$. Diffusion equation on a disk.

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### April 7: Bessel functions and applications. Finished Lecture Note 14.

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# Announcements For MATH 400

### Office Hours: Every Monday, Wednesday, Friday, 4:30pm-5:20pm, LSK 303B. Starting Date: Jan. 6

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### Midterm date: Feb. 23, 2016, in class. Coverage: whatever before the term break.

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### Revised due date for assignment 3: Feb. 22

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### Coverage of Midterm test: up to Lecture Note 6.

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### No Office Hours on March 21, March 23.

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### From April 11 to April 15, and April 18, 19, I shall be in my office from 10am to 4pm. If you have questions, please knock on my door or send me an email.

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### Final Exam: April 20, 2016, 08:30AM, LSK 201