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
Downloads For MATH400
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.