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
Downloads For MATH400
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.
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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