Lectures on Fourier series
著者
書誌事項
Lectures on Fourier series
（Oxford science publications）
Oxford University Press, 1988
- : pbk
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注記
Includes index
内容説明・目次
内容説明
A short introductory book, examining Fourier series which is seen as indispensable in describing periodic phenomena to various degrees of approximation. Jean Baptiste Joseph Fourier, who gave his name to the series taught at France's foremost school of engineering and was Governor of Lower Egypt and had various administrative positions in France, both under Napoleon and under the Bourbons. The ideas are introduced slowly with the aid of a large number of worked examples and is aimed at students in engineering, physics and chemistry. This book is based on a lecture course in the Department of Engineering at Oxford taught by the author. Solymar is the co-author of "Lectures on Electromagnetic Theory" (1983) and "Lectures on the Electrical Properties of Materials 4/e" (1988). He has also written a "Solutions Manual" (1988) to accompany the latter book.
目次
- Introduction: on approximations
- approximation to a cosine function
- periodic functions. Part 1 Finding the Fourier series: derivation of the coefficients
- symmetry considerations
- how to sum up a series
- differentiation and integration
- the coefficients for arbitrary period
- the Fourier series as optimum approximation
- full-range, half-range, quarter-range, etc
- exponential form
- Parseval's theorem
- filters. Part 2 Forced solutions of ordinary differential equations with periodic excitation: first-order differential equations
- second-order differential equations
- higher-order differential equations
- examples from electrical engineering
- solution of a non-linear differential equation
- exercises. Part 3 Partial differential equations: the vibrating string
- heat conduction
- transmission lines
- exercises. Appendix: the Gibbs phenomenon.
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