文档介绍：i i
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Mathematical
Methods in Physics
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Mathematical
Methods in Physics
Partial Differential Equations,
Fourier Series, and Special Functions
Victor Henner
Tatyana Belozerova
Kyle Forinash
A K Peters, Ltd.
Wellesley, Massachusetts
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Editorial, Sales, and Customer Service Office
A K Peters, Ltd.
888 Worcester Street, Suite 230
Wellesley, MA 02482
Copyright c 2009 by A K Peters, Ltd.
All rights reserved. No part of the material protected by this copyright
notice may be reproduced or utilized in any form, electronic or mechani-
cal, including photocopying, recording, or by any information storage and
retrieval system, without written permission from the copyright owner.
Library of Congress Cataloging-in-Publication Data
Henner, Victor.
Mathematical methods in physics : partial differential equations, Fourier series,
and special functions / Victor Henner, Tatyana Belozerova, Kyle Forinash.
p. cm.
Includes bibliographical references and index.
ISBN 978-1-56881-335-6 (alk. paper)
1. Mathematical physics–Textbooks. I. Belozerova, Tatyana. II. Forinash,
Kyle. III. Title.
2009
–dc22
2008022076
Printed in India
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To Bruce Adams,
a great friend
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Contents
Introduction xi
1 Fourier Series 1
Periodic Processes and Periodic Functions . . . . . . . . 1
Fourier Formulas . . . . . . . . . . . . . . . . . . . . . 3
Orthogonal Systems of Functions . . . . . . . . . . . . . 7
Convergence of Fourier Series . . . . . . . . . . . . . . 9
Fourier Series for Nonperiodic Functions . . . . . . . . 16
Fourier Expansions on Intervals of Arbitrary Length . . . 16
Fourier Series in Cosine or Sine Functions . . . . . . . . 18
plex Form of the Fourier Series . . . . . . . . . 30
Generalized Fourier Series . . . . . . . . . . . 3