Early Fourier analysis
著者
書誌事項
Early Fourier analysis
(The Sally series, . Pure and applied undergraduate texts ; 22)
American Mathematical Society, c2014
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注記
Includes bibliographical references (p. 377-381) and index
内容説明・目次
内容説明
Fourier Analysis is an important area of mathematics, especially in light of its importance in physics, chemistry, and engineering. Yet it seems that this subject is rarely offered to undergraduates. This book introduces Fourier Analysis in its three most classical settings: The Discrete Fourier Transform for periodic sequences, Fourier Series for periodic functions, and the Fourier Transform for functions on the real line.
The presentation is accessible for students with just three or four terms of calculus, but the book is also intended to be suitable for a junior-senior course, for a capstone undergraduate course, or for beginning graduate students. Material needed from real analysis is quoted without proof, and issues of Lebesgue measure theory are treated rather informally. Included are a number of applications of Fourier Series, and Fourier Analysis in higher dimensions is briefly sketched. A student may eventually want to move on to Fourier Analysis discussed in a more advanced way, either by way of more general orthogonal systems, or in the language of Banach spaces, or of locally compact commutative groups, but the experience of the classical setting provides a mental image of what is going on in an abstract setting.
目次
Background
Complex numbers
The discrete Fourier transform
Fourier coefficients and first Fourier series
Summability of Fourier series
Fourier series in mean square
Trigonometric polynomials
Absolutely convergent Fourier series
Convergence of Fourier series
Applications of Fourier series
The Fourier transform
Higher dimensions
Appendix B. The binomial theorem
Appendix C. Chebyshev polynomials
Appendix F. Applications of the fundamental theorem of algebra
Appendix I. Inequalities
Appendix L. Topics in linear algebra
Appendix O. Orders of magnitude
Appendix T. Trigonometry
References
Index
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