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.


Lecture Notes For MATH400-101


Lecture Notes 1

(revised) Example 10 (in Lecture 1)

Lecture Notes 2

Lecture Notes 3

Summary of 1st Order PDE

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

Download 2: HW1 (Due: Sept. 16, by 6pm)

Download 3: Solutions to HW1 (Due: Sept. 16, by 6pm)

Download 4: HW2 (Due: Sept. 27, by 6pm)

Download 5: Solutions to HW2 (Due: Sept. 27, by 6pm)

Download 6: HW3 (Due: Oct. 8, by 6pm)

Download 7: Old Midterm I

Download 8: Solutions to Old Midterm I

Download 9: Old Midterm I and Solutions

Download 10: Solutions to HW3

Download 11: Solutions to Midterm I

Download 12: HW4 (Due: Oct. 25, by 6pm)

Download 13: HW5 (Due: Nov.6, by 6pm)

Download 14: Solutions to HW4

Download 15: HW6 (Due: Nov.25, by 6pm)

Download 16: Solutions to HW5

Download 17: Old Midterm II

Download 18: Formula for Midterm II

Download 19: Solutions to Midterm II

Download 20: HW7 (Due: Dec. 3, by 7pm)

Download 21: Solutions to HW6

Download 22: Solutions to HW7

Download 23: Old Final I

Download 24: Solutions to Old Final I

Download 25: Old Final II

Download 25: Solutions to Old Final II

Download 26: Old Final III and its solutions

Download 27: Final Review

Download 28: Final Exam Solutions

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.

Sept. 18: Lecture Note 2: Expansion fans, shock curves. Rankine-Hugoniot condition.

Sept. 20: Lecture Note 2. Two examples of expansion fan and shock curves. Traffic model.

Sept. 23: Traffic model. Lecture Notes 2. Start of Lecture Note 3--derivations of Charpit's equation.

Sept. 25: Examples of fully nonlinear 1st order PDE. Completion of Lecture Notes 3.

Summary of 1st Order PDE

Sept. 27: Summary of 1st order PDE. Examples of second order PDEs. Divergence theorem.

Sept. 30: PDE problems. Well-posedness. Examples of well-posedness and ill-posedness.

Oct. 2: Types of Second Order Linear PDEs. Linear Transformations. Lecture Note 4 is finished.

Oct. 4: General solutions of hyperbolic equations---decomposition of 1st order operators. d'Alembert's formula. Lecture Note 5.

Oct. 7: Geometric Meaning of wave equation. Wave equation in a Quarter Plane.

Oct. 9: Properties of Wave equation: domain of influence, domain of dependence, energy conservation. Wave equation with source.

Oct. 11: Midterm One.

Oct. 16: Wave equation with source. Method of reflection.

Oct. 18: Method of Reflection for interval. Diffusion equation. ODE.

Oct. 21: Solution formula for diffusion equation. Fundamental solution. Error function. Examples.

Oct. 23: Diffusion with source. Well-posedness. Comparison of wave and diffusion.

Oct. 25: Diffusion with boundary conditions. Method of extension. Start on Lecture Note 9.

Oct. 28: Dirichlet Boundary Conditions.

Oct. 30: Neumann Boundary Conditions. Robin Boundary Conditions.

Nov. 1: Eigenvalue problems with Robin boundary conditions. Lecture Note 9.5.

Nov. 4: Heat equation with Robin boundary condition. Standard form of Sturm-Liouville eigenvalue problem.

Nov. 6: Sturm-Liouville Eigenvalue Problems and heat equation. Several examples. Ended with Bessel function of order zero.

Nov. 8: Bessel function of order zero. Heat equation with inhomogeneous source and boundary conditions. (End of coverage of Midterm II.)

Nov. 13: Wave equation with inhomogeneous sources. Method of Shifting Data. Laplace equation: Uniqueness by Energy Method.

Nov. 15: Midterm II.

Nov. 18: Laplace equation in rectangles and cubes.

Nov. 20: Heat equation in rectangles. Laplace equation in a disk.

Nov. 22: Poisson's formula. Mean-value-property. Max-mIn principle.

Nov. 25: Applications of mean-value-property, Max-Min principle. Annulus. Exterior of a disk. Wedge.

Nov. 27: Laplace in a wedge. heat equation in two-dimensional disks. Bessel functions of order n. Lecture Notes 14.

Nov. 29: Laplace equation in 3D: cylindrical coordinates and spherical coordinates. Legendre polynomials. Lecture Note 15.

Dec. 14: 8:30am-11am, BUCH B313, Final Exam


Announcements For MATH 400-101


New office Hours on September 27: 3-6pm

Office Hours in the week of September 30-Oct. 4: Oct. 2, 2-3pm, Oct. 3, 10-4pm, Oct. 4 2-3pm.

New deadline for HW2--Oct 8

Office hours in the exam period: Dec. 2, 3, Dec. 9-13.


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