Linear Methods of Applied Mathematics
Orthogonal series, boundary-value problems, and integral operators

Evans M. Harrell II and James V. Herod

© Copyright 1994,1995,1996, 1997, 2000 by Evans M. Harrell II and James V. Herod. All rights reserved.

This is a WWW textbook written by Evans M. Harrell II and James V. Herod, both of Georgia Tech. It is suitable for a first course on partial differential equations, Fourier series and special functions, and integral equations. Students are expected to have completed two years of calculus and an introduction to ordinary differential equations and vector spaces. For recommended 10-week and 15-week syllabuses, read the preface.

This text concentrates on mathematical concepts rather than on details of calculations, which are often done with software, such as Maple or Mathematica. It is not necessary to have experience with Maple or Mathematica in order to read this text, nor is it the goal of this text to teach software, but there are links in the text to Maple worksheets and Mathematica notebooks, which perform calculations and provide some supplementary instructive material. The supplementary material exists both in a "flat" form, which can be read with Netscape, and also in an active form, requiring mathematical software.

If you have access to mathematical software, you may wish to take this opportunity to set up the latest version of Netscape to launch Mathematica or Maple automatically when appropriate.

You are welcome to browse, but if you make more than casual use, such as downloading files or using them as study materials, certain restrictions and fees apply. Before proceeding, please read this copyright notice.

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Contents


     Preface
     Diagnostic quiz

       Please take this before embarking on a course from this book.

       Links to review materials on ordinary differential equations and linear algebra

  1. Linearity

       Also available in an Adobe Acrobat version

  • The geometry of functions

    •        Also available in an Adobe Acrobat version

           The red syllabus and the yellow syllabus continue with Chapter III
           The green syllabus continues with Chapter XIII

  • Fourier series. Introduction.

    •        Also available in an Adobe Acrobat version (without links)

  • Calculating Fourier series.

    •        Also available in an Adobe Acrobat version (without links)
          A test at this stage.

  • Differentiating Fourier series.

    •        Also available in an Adobe Acrobat version (without links)

           The red syllabus continues with Chapter VI
           The yellow syllabus continues with Chapter XIII

  • Notes on a vibrating string.

    •        Also available in an Adobe Acrobat version (without links)

  • Traveling waves.

    •        Also available in an Adobe Acrobat version (without links)

          A test at this stage.
  • Mathematics of hot rods.

    •        Also available in an Adobe Acrobat version (without links)

  • PDEs in space. (includes potential equations)

    •        Also available in an Adobe Acrobat version (without links)

  • PDEs on a disk.

    •        Also available in an Adobe Acrobat version (without links)

          A test at this stage.
  • Great balls of PDEs.
  • Hunting for eigenvalues.

    •        End of the red syllabus.

  • Geometry and integral operators.
  • Solving Y = KY + f.
          A test at this stage.
  • Ordinary differential operators.
  • Finding Green functions for ODEs.
          A test at this stage.
  • Green functions, Fourier series, and eigenfunctions.
  • Partial differential operators - classification and adjoints.
  • The free Green function and the method of images
          A test at this stage.
  • The fundamental solution of the heat equation
  • Using conformal mapping to construct Green functions.
  • Some advanced topics.
    APPENDICES
    EXTERNAL LINKS

    (We do not maintain these and cannot guarantee their content)
    Index and glossary.

    • Link to

    Evans M. Harrell II (send message)
    James V. Herod (send message)