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Fourier Series and Orthogonal Functions (63 Edition)

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Fourier Series and Orthogonal Functions (63 Edition) Cover

 

Synopses & Reviews

Please note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the publisher comments.

Publisher Comments:

This incisive text deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. Directed to advanced undergraduate and graduate students in mathematics as well as in physics and engineering, the book requires no prior knowledge of partial differential equations or advanced vector analysis. Students familiar with partial derivatives, multiple integrals, vectors, and elementary differential equations will find the text both accessible and challenging.

The first three chapters of the book address linear spaces, orthogonal functions, and the Fourier series. Chapter 4 introduces Legendre polynomials and Bessel functions, and Chapter 5 takes up heat and temperature. The concluding Chapter 6 explores waves and vibrations and harmonic analysis. Several topics not usually found in undergraduate texts are included, among them summability theory, generalized functions, and spherical harmonics.

Throughout the text are 570 exercises devised to encourage students to review what has been read and to apply the theory to specific problems. Those preparing for further study in functional analysis, abstract harmonic analysis, and quantum mechanics will find this book especially valuable for the rigorous preparation it provides. Professional engineers, physicists, and mathematicians seeking to extend their mathematical horizons will find it an invaluable reference as well.

Synopsis:

An incisive text combining theory and practical example to introduce Fourier series, orthogonal functions and applications of the Fourier method to boundary-value problems. Includes 570 exercises. Answers and notes.

Synopsis:

This incisive text, directed to advanced undergraduate and graduate students in mathematics, physics and engineering, deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. 570 exercises.

Table of Contents

1. Linear Spaces

  1.1 Functions

  1.2 Vectors

  1.3 Linear Spaces

  1.4 Finite-dimensional Linear Spaces

  1.5 Infinite-dimensional Linear Spaces

2. Orthogonal Functions

  2.1 Inner Products

  2.2 Orthogonal Functions and Vectors

  2.3 Orthogonal Sequences

  2.4 Differential Operators

  2.5 Integral Operators

  2.6 Convolution and the Dirichlet Kernel

3. Fourier Series

  3.1 Motivation

  3.2 Definitions

  3.3 Examples of Trigonometric Series

  3.4 Sine and Cosine Series

  3.5 The Gibbs Phenomenon

  3.6 Local Convergence of Fourier Series

  3.7 Uniform Convergence

  3.8 Convergence of Fourier Series

  3.9 Divergent Series

  3.10 Generalized Functions

  3.11 Practical Remarks

4. Legendre Polynomials and Bessel Functions

  4.1 Partial Differential Equations

  4.2 The Intuitive Meaning of the Laplacian Operator

  4.3 Legendre Polynomials

  4.4 Laplace's Equation in Spherical Coordinates

  4.5 Spherical Harmonics

  4.6 Bessel Functions

5. Heat and Temperature

  5.1 Theory of Heat Conduction

  5.2 Temperature of Plates

  5.3 Temperature of Solids

  5.4 Harmonic Functions

  5.5 Existence Theorems

  5.6 Heat Flow

6. Waves and Vibrations, Harmonic Analysis

  6.1 The Vibrating String

  6.2 The One-dimensional Wave Equation

  6.3 The Weighted String

  6.4 String with Variable Tension and Density

  6.5 Vibrating Membranes

  6.6 Waves in Two and Three Dimensions

  6.7 The Fourier Integral

  6.8 Algebraic Concepts in Analysis

  Supplementary Exercises

Appendix. Functions on Groups

  Answers and Notes; Index

Product Details

ISBN:
9780486659732
Author:
Davis, Harry F.
Publisher:
Dover Publications
Author:
Mathematics
Location:
New York :
Subject:
General
Subject:
Physics
Subject:
Mathematical Physics
Subject:
Fourier series
Subject:
Functions, orthogonal
Subject:
General Mathematics
Subject:
Mathematical Analysis
Subject:
Mathematics - General
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
n.p0s7
Publication Date:
19890531
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
416
Dimensions:
8.5 x 5.38 in 1.05 lb

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Related Subjects


Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Fourier Analysis
Science and Mathematics » Mathematics » General
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Science and Mathematics » Physics » General
Science and Mathematics » Physics » Math

Fourier Series and Orthogonal Functions (63 Edition) Used Trade Paper
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Product details 416 pages Dover Publications - English 9780486659732 Reviews:
"Synopsis" by ,
An incisive text combining theory and practical example to introduce Fourier series, orthogonal functions and applications of the Fourier method to boundary-value problems. Includes 570 exercises. Answers and notes.

"Synopsis" by ,
This incisive text, directed to advanced undergraduate and graduate students in mathematics, physics and engineering, deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. 570 exercises.
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