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.

Lecture Notes For MATH400

Lecture Notes 1

Lecture Notes 2

Lecture Notes 3

Lecture Notes 4

Lecture Notes 5

Lecture Notes 6

Lecture Notes 7

Lecture Notes 8

Lecture Notes 9

Lecture Notes 9.5

Lecture Notes 10

Lecture Notes 11

Lecture Notes 12

Lecture Notes 13

Lecture Notes 14

Downloads For MATH400

Download 1: Syllabus

Download 2: Assignment One (due date: Jan. 19, 2016)

Download 3: Exercises (No need to hand in)

Download 4: Assignment Two (due date: Feb. 2, 2016)

Download 5: Solutions to Assignment One

Download 6: Assignment Three (due date: Feb. 22, 2016)

Download 7: Solutions to Assignment Two

Download 8: Exercises (No need to hand in)

Download 9: Old Midterm (2014)

Download 10: Solutions to Old Midterm

Download 11: Midterm

Download 12: Solutions to Midterm

Download 13: Solutions to Assignment 3

Download 14: Assignment Four (due date: March 8th, 2016)

Download 15: Solutions to Assignment 4

Download 16: Assignment 5 (due date: March 18, 2016)

Download 17: Solutions to Assignment 5

Download 18: Assignment 6 (due date: March 31, 2016)

Download 19: Solutions to Assignment 6

Download 20: Assignment 7 (due date: April 14, 2016)

Download 21: A complete list of formula and summary of Theorems

Download 22: Solutions to Assignment 7

Updates For MATH 400

Jan. 4: Method of Characteristics.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

March 29: Poisson formula. Applications.

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

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

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

Announcements For MATH 400

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

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

Revised due date for assignment 3: Feb. 22

Coverage of Midterm test: up to Lecture Note 6.

No Office Hours on March 21, March 23.

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.

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


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