Fourier Series and Boundary Value Problems

1.	Fourier Series
  1.1    Orthogonality of vectors
  1.2    Orthogonality of functions
  1.3    Trignometric Identities
  1.4    Orthogonality of sines and cosines
  1.5    Fourier cosine series
            1.5.1    Theory
            1.5.2    Calculations with Mathematica
  1.6    Fourier sine series
            1.6.1    Theory
            1.6.2    Calculations with Mathematica
  1.7    Fourier series
            1.7.1    Theory
            1.7.2    Calculations with Mathematica
  1.8    Relationships between the various Fourier Series
            1.8.1    Theory
            1.8.2    Calculations with Mathematica
  1.9    Fourier series on other intervals
            1.9.1    Fourier series on other intervals
            1.9.2    Calculations with Mathematica
  1.10   Complex form of Fourier Series
 
2.	Differential Equations and Boundary Value Problems
  2.1    The heat equation
  2.2    Laplace's equation
  2.3    Cylindirical coordinates
  2.4    Spherical coordinates
  2.5    The wave equation
  2.6    DAlemberts solution of the wave equation
  
3.	Solution of Boundary Value Problems using Fourier Series
  3.1    Second order constant coefficient eqns
  3.2    Solving the heat equation using separation of variables
            3.2.1    Theory
            3.2.2    Calculations with Mathematica
  3.3    Solving the wave equation using separation of variables
  3.4    Inhomogeneous equations
  3.5    Inhomogeneous boundary conditions
  3.6    Dirichlet problems
  
4.	Convergence of Fourier Series
  4.1    Piecewise smooth functions
  4.2    The Fourier coefficients approach zero
  4.3    Partial sum of Fourier series and the Dirichlet kernel
  4.4    Convergence of Fourier series
  
5.	Finite Fourier Series
  5.1    Trigonometric sums
  5.2    Orthogonality of discrete trigonometric functions
  5.3    Discrete fourier series
  5.4    Examples
            5.4.1    Examples
            5.4.2    Calculations with Mathematica
  5.5    Complex form of discrete Fourier Series

6.	Fourier Integrals
  6.1    From Fourier series to Fourier integrals
  6.2    More examples
  6.3    Complex form of the Fourier integral - the Fourier transform
  6.4    Fourier integral table
  6.5    The heat equation in an infinite rod

7.	Fourier - Bessel Series

     An Introduction to Mathematica

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