Math 124 A,B, Syllabus
Partial Differential Equations, Fourier Transform and Numerical Methods

• The Wave Equation
  • Characteristics in one dimension
  • The D'Alembert Solution

• The Heat Equation
  • Fourier integrals
  • The heat kernal on the line
  • Schrödinger's equation

• The Potential Equation
  • The Dirichlet and the Neumann problems
  • Green's identities
  • Poisson's equation

• Generalized Functions
  • Calculus of distributions
  • The wave equation in one and two dimensions

• The Fourier Series
  • The Lebesque integral
  • Hilbert space
  • Seperation of variables

• Applications
  • The heat equation on the interval
  • The wave equation on the interval
  • The potential equation in a box
  • The Schrödinger equation and Sturm-Liouville theory

• Numerical Methods
  • Finite Differences
  • The Fast Fourier Transform
  • Finite Elements

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