Linear Methods of Applied Mathematics

Evans M. Harrell II and James V. Herod*

*(c) Copyright 1994-2000 by Evans M. Harrell II and James V. Herod. All rights reserved.

version of 9 October 2000

Index and glossary

For background information on people referred to, look at the file with brief biographies.

• adjoint,
            integral operator
            matrix
            ordinary differential operator
            partial differential operator, formal
• a.e. (almost everywhere)
• alternative theorem,
            for integral operators
            for matrices
            for ordinary differential operators
• ansatz
• Bessel's equation
• Bessel function
      , nodes or zeroes of
• , Dirichlet
            , Neumann
            , periodic
• boundary-value problem
• Cauchy-Schwarz-Buniakovskii inequality
• classification of partial differential operators
• colatitude
• complete (in Chapter III) (in Chapter X)
• d'Alembert's solution
• d'Alembertian
• delta function
• diffusion equation
• distribution
• eigenvalue equation
• elliptic partial differential operator
• Euler's equidimensional equation
• Euler's formula
• filtering
• Fourier coefficients
•           , uniqueness of
• Fourier series; see also chapter 2
            , cosine; see also chapter 2
            , exponential
            , multiple
            , powerful theorem on
            , sine; see also chapter 2
• Fourier-Bessel series
• Fredholm alternative theorem,
            for integral operators
            for matrices
            for ordinary differential operators
• Fredholm integral equation
• function space
• generalized function
• generalized solution
• Gibbs' phenomenon
• Gram-Schmidt procedure
• Green function,
  
  free
• harmonic function
• heat capacity, conductivity
• heat equation (Chapter VI) (Chapter VIII) (Chapter X) (derivation)
• heat kernel
• Heaviside function
• hyperbolic partial differential operator
• images, method of.
• indicator function
• inner product
• jump discontinuity for a Green function
• kernel (of integral operator)
• integral equation integral operator
• L² (function space)
• L² norm (for function space)
• Laplace's equation, Chapter VI, Chapter IX
• Laplace operator
• Legendre polynomials
  
  associated (more about)
  spherical harmonics
• linear combination
• linear transformation (=linear operator)
• maximum principle,
  for the heat equation
  for the potential equations
• Clerk Maxwell's equations
• mean-value theorem for potential equations
• mod
• operator
• norm
• Poisson's equation
• potential equation
• product solution
• superposition
• support
• uniqueness theorem
• weak solution
• test function
• well-posed problem