Homepage for Elementary Partial Differential Equations 423:01, Fall 2003

 




Final exam: 

Tuesday, December 16, 8-11 PM   SEC 207
Review session  Thursday Dec. 11, 6:10 PM  Sec 211

Final exam Practice problems (newest version, typo corrected)

 2nd midterm Practice problems

 1st midterm Practice problems


General Course Information


  Approximate Syllabus


Even, Odd, Periodic and Complex-valued functions.Even, Odd, Periodic and Complex-valued functions.Even, Odd, Periodic and Complex-valued functions.
 

Lecture Date Topics covered Sections fromText
1 09-02 What is a Partial Differential Equation? 1.1
2 09-04
 First-order Linear Equations (Solution in the constant-coefficient case; the variable-coefficient case and characteristic curves. 1.2
3 09-09
 Flows, Vibrations and Diffusions (Derivations of PDEs in various physical situations; e.g., the vibrating string, the vibrating drumhead, diffusion, heat flow, hydrogen atom). 1.3
4 09-11
 Initial and boundary conditions (the Dirichlet, Neumann and Robin conditions and their significance for the vibrating string and diffusion equations.  Conditions at infinity.) 1.4
5 09-16 Well- (and ill-)Posed Problems. 1.5
6 09-18
 Types of second-order equations. 1.6
7 09-23 The Wave Equation (D'Alembert's solution on the line; the plucked string). 2.1
8 09-25 Causality and Energy. 2.2
9 09-30 The Diffusion (or Heat) Equation (the maximum principle; uniqueness for the Dirichlet problem). 2.3
10 10-02 Diffusion on the whole real line (the Gaussian or fundamental solution). 2.4
11 10-07 First Midterm--regular class hour and location; covers 1.1 through 2.3
12 10-09 Comparison of waves and diffusion. 2.5
13 10-14
 Separation of Variables, the Dirichlet Condition (both for the wave and the diffusion equations). 4.1
14 10-16
 The Neumann Condition. 4.2
15 10-21 Robin's Conditions (cases in which zero is an eigenvalue and cases in which one eigenvalue is negative). 4.3
16 10-23 The Coefficients (or discrete Fourier transform): formulas for the coefficients, applications to the wave and the diffusion equations. 5.1
17 10-28  Even, Odd, Periodic and Complex-valued functions. 5.2
18 10-30 Orthogonality and "General Fourier Series" (orthogonal systems from symmetric boundary conditions; complex eigenvalues) 5.3
19 11-04 Completeness (three notions of convergence: pointwise, uniform and mean-square: convergence results for Fourier series and their generalizations). 5.4
20 11-06 Completeness and the Gibbs phenomenon. (Nice applet illustration) 5.5
21 11-11 Second Midterm--regular class hour and location; covers 2.4 through 5.4
22 11-13 Inhomogeneous Boundary Conditions. 5.6
23 11-18 The Laplace Equation (its physical significance, maximum principle, uniqueness of solutions of the Dirichlet Problem, invariance of the Laplace operator under rigid motions). 6.1
24 11-20 Rectangles and Cubes. 6.2
25 11-25 Green's First Identity (and some consequences). 7.1
26 12-02 Green's Second Identity (and some consequences). 7.2
27 12-04 Green's Functions and the Dirichlet Problem. 7.3
28 12-09 Half-Spaces and Spheres. 7.4