MATH400-101 :       Applied Partial Differential Equations   (First term 2018-2019)


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, Friday, 12-1pm, 4:30pm-5:30pm, LSK 303B.


Lecture Notes For MATH400-101


Lecture Notes 1

Lecture Notes 2

Lecture Notes 3

Summary on First Order PDEs

Lecture Notes 4

Lecture Notes 5

Lecture Notes 6

Method of Reflection on Intervals

Lecture Notes 7

Lecture Notes 8

Lecture Notes 8.5

Lecture Notes 9

Lecture Notes 9.5

Lecture Notes 10

Notes on Second Order ODEs

Lecture Notes 11

Lecture Notes 12

Lecture Notes 13

Lecture Notes 14

Lecture Notes 15


Downloads For MATH400


Download 1: Syllabus

Homework Assignment 1 (due: 6pm, September 17, 2018)

Homework Assignment 2 (due: 6pm, September 28, 2018)

Solutions to Homework Assignment 1

Homework Assignment 3 (due: 6pm, October 9, 2018)

Formula for Problem 6 of Homework Assignment 3

Solutions to Homework Assignment 2

Old Midterm 1

Solutions to Old Midterm 1

Solutions to Homework Assignment 3

Solutions to Midterm I

Homework Assignment 4 (due: 6pm, October 26, 2018; revised)

Solutions to Homework Assignment 4

Homework Assignment 5 (due: 6pm, November 6th, 2018)

Solutions to Homework Assignment 5

Homework Assignment 6 (due: 6pm, November 20th, 2018)

Formula (up to Midterm 2)

Solutions to Problems 1-3 of Assignment 6

Solutions to Assignment 6

Solutions to Midterm 2

Homework Assignment 7 (last one) (due: 6pm, December 4th, 2018)

Old Final Exam (I) Solutions to Old Final Exam (I)

Old Final Exam (II) Solutions to Old Final Exam (II)

Final Review

Solutions to Assignment 7

Updates For MATH 400


First class: Sept 5, 2018

Sept 5: 1st order PDE, characteristic curves, data curvae. Example $u_x=0$.

Sept 7: Domain of existence. ODEs for characteristic curves. Steps of solving $ a(x,y) u_x+ b(x, y) u_y=0$.

Sept 10: Examples of $ a(x,y)+ b(x, y) u_y=0$. Example 6 of Lecture Note 1. Begin $ a(x, y) u_x+ b(x,y) u_y= c(x, y, u)$.

Sept 12: Examples of solving $ a u_x+b u_y= d(x,y, u)$. Please replace Example 10 in Lecture Note 1 Example 10 (Lecture 1)

Sept. 17: Quaslinear first order PDEs. $ u_t+ c(u) u_x=0$. examples and general solutions. Break-down time $ t= t_B$.

Sept 19: Rankine-Higoniot formula for shock curve. Expansion fan. Examples.

Sept. 21: Examples of quaislinear 1st order PDE with both expansion fan and shock curves.

Sept. 24: Traffic model examples. Finish Lecture Note 2.

Sept. 26: lecture note 3--fully nonlinear 1st order PDE.

Sept. 28: Derivation of heat and wave equation.

Oct. 1: PDE problems. Well-posedness.Lecture Note 4.

Oct. 3: Classification of types and linear transformations to standard form.

Oct. 5: d'Alembert's formula by decomposing into two first order operators.

Oct. 10: Domain of influence, domain of dependence. Inhomogenneous Wave equation.

Oct. 12: Midterm I.

Oct. 15: Well-posedness of wave equation. Energy of wave equation.

Oct. 17: Method of Reflection on Wave equations. Method of Reflection on Intervals

Oct. 19: Heat equation. Derivation the formula for initial value problem of heat equation. Lecture note 7-8.

Oct. 22: Example of formula of heat equation. Lecture note 8.

Oct. 24: Well-posedness of heat equation. Comparison between wave and heat equation. heat equation with source, on half line.

Oct. 26: Method of Separation of Variables for heat equation with Dirichlet boundary conditions.

Oct. 29: Method of separation of variables: Robin boundary conditions.

Oct. 31: Eigenvalues for Robin boundary conditions. Lecture note 9.5.

Nov. 2: Heat equation with Robin boundary conditions. Sturm-Liouville Eigenvalue Problem.

Nov. 5: Sturm-Liouville Eigenevalue Problems. General Properties. Examples

Nov. 7: Eigenvalues of Sturm-Liouville. Bessel function of order zero.

Nov. 9: Sturm-Liouville. Heat equation with inhomogeneous.

Nov. 14: Heat equation with inhomogenenous source. Laplace equation. Uniqueness. Lecture Note 12.

Nov. 16: Midterm II.

Nov. 19: Method of separation of variables for Laplace equation in case: rectangles and cubes. heat equation in Cartesian coordinates.

Nov. 21: Laplace equation in a disk.

Nov. 23: Poisson's formula and applications to Maximum Principle.

Nov. 26: Laplace equation in annulus, exterior domains, wedge, sector.

Nov. 28: Higher dimensional heat equations in rectangles and disk. Bessel functions of order n. Completed Lecture 14.

Nov. 30: Bessel function of order $n$, inhomogeneous wave equation in higher dimensions.


Announcements For MATH 400


New due date for HW2: by 6pm, September 28, 2018.

The 4:30-5:30pm office hour on Oct.1 is cancelled.

New due date for HW3: by 6pm, October 9, 2018.

Coverage of Midterm 1: first order PDEs, and second order up to classes on Oct. 5.

New Office Hours; Dec. 3, 4, 17, 18.


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