Early Fourier Analysis

Inbunden, Engelska, 2015

1 319 kr

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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.

Produktinformation

Utgivningsdatum2015-02-28
Mått178 x 254 x undefined mm
Vikt851 g
FormatInbunden
SpråkEngelska
SeriePure and Applied Undergraduate Texts
Antal sidor390
FörlagAmerican Mathematical Society
ISBN9781470415600

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Beräkning och matematisk analys inom Naturvetenskap och teknik

BackgroundComplex numbersThe discrete Fourier transformFourier coefficients and first Fourier seriesSummability of Fourier seriesFourier series in mean squareTrigonometric polynomialsAbsolutely convergent Fourier seriesConvergence of Fourier seriesApplications of Fourier seriesThe Fourier transformHigher dimensionsAppendix B. The binomial theoremAppendix C. Chebyshev polynomialsAppendix F. Applications of the fundamental theorem of algebraAppendix I. InequalitiesAppendix L. Topics in linear algebraAppendix O. Orders of magnitudeAppendix T. TrigonometryReferencesIndex

Hugh Montgomery has written a book which both students and faculty should appreciate. I wish it had been written 15 years ago so I could have shared it with students. It is a gem." - Richard Askey, University of Wisconsin-Madison, USA"Montgomery has written an exquisite text combining basic material, exciting examples, advanced topics, wonderful historical notes, and excellent exercises. It is absolutely compelling and masterful!" - John Benedetto, University of Maryland, USA"This nice book is likely to be especially successful. l feel that the author has managed admirably to bring to light both the beauty and the usefulness of Fourier's idea, thus making the first introduction to Fourier analysis a joy for undergraduates. All the details are included in a way that is both attractive and easy for students to follow." - Palle Jorgensen, University of Iowa, USA, Author of Wavelets Through a Looking Glass