Course Description

Classical representation and convergence theorems for Fourier series; method of separation of variables for the solution of the one-dimensional heat and wave equation; the heat and wave equations in higher dimensions; eigenfunction expansions; spherical a nd cylindrical Bessel functions; Legendre polynomials; methods for evaluating asymptotic integrals (Laplace's method, steepest descent); Laplace's equation and harmonic functions, including the maximum principle. As time permits, additional topics will be selected from: Fourier and Laplace transforms; applications to linear input-output systems, analysis of data smoothing and filtering, signal processing, time-series analysis, and spectral analysis; dispersive wave equations; the method of stationary phas e; the method of characteristics.

Textbook

Syllabus

• Download SECTION 1 syllabus: (PDF)
  
  
• Download SECTION 2 syllabus: (PDF)
  

MATLAB Help

• Download guide to MATLAB plotting [MSCC, University of Washington, 1996]: (PDF)
  
  
• Download MATLAB tutorial: (PDF)
  
  
• Go to the MATLAB Help Desk at the MathWorks site.
  This allows you to search for a specific MATLAB function.
  
  

Homework

Handouts

• 1D Heat Equation
  • Figure 1: (PDF) solution to heat equation example
  • Figure 2: (PDF) difference between exact solution and first term in infinite series solution

• 1D Heat Equation -- Discontinuous Initial conditions
  • Figure 1: (PDF) Example #1
  • Figure 2: (PDF) Example #2

• 1D Wave Equation Example (PDF)

• 2D Vibrating Membrane
  • Figure 1: memb1.jpg
  • Figure 2: memb2.jpg
  • Figure 3: memb3.jpg
  • Figure 4: memb4.jpg
  • Figure 5: memb5.jpg
  • Figure 6: memb6.jpg
  • MATLAB file to generate PLOTS: membrane.m