Linear Methods of Applied Mathematics free book

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

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

Links to review materials on

ordinary differential equations and

linear algebra

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)
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)
test at this stage.

Mathematics of hot rods.
Also available in an
Adobe Acrobat version

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)

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

Geometry and integral operators.
Solving Y = KY + f.
test at this stage.

Ordinary differential operators.
Finding Green functions for ODEs.
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
test at this stage.
The fundamental solution of the heat equation
Using conformal mapping to construct Green functions.
Some advanced topics.

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