The Evolution of Applied Harmonic Analysis: Models of the Real World

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Springer Science & Business Media, Nov 22, 2013 - Mathematics - 351 pages

"...can be thoroughly recommended to any reader who is curious about the physical world and the intellectual underpinnings that have lead to our expanding understanding of our physical environment and to our halting steps to control it. Everyone who uses instruments that are based on harmonic analysis will benefit from the clear verbal descriptions that are supplied."

— R.N. Bracewell, Stanford University

A sweeping exploration of essential concepts and applications in modern mathematics and science through the unifying framework of Fourier analysis! This unique, extensively illustrated book describes the evolution of harmonic analysis, integrating theory and applications in a way that requires only some general mathematical sophistication and knowledge of calculus in certain sections.

Key features:

* Historical sections interwoven with key scientific developments showing how, when, where, and why harmonic analysis evolved

* Exposition driven by more than 150 illustrations and numerous examples

* Concrete applications of harmonic analysis to signal processing, computerized music, Fourier optics, radio astronomy, crystallography, CT scanning, nuclear magnetic resonance imaging and spectroscopy

* Includes a great deal of material not found elsewhere in harmonic analysis books

* Accessible to specialists and non-specialists

The Evolution of Applied Harmonic Analysis will engage graduate and advanced undergraduate students, researchers, and practitioners in the physical and life sciences, engineering, and mathematics.

 

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Contents

The Man and the Mathematician
1
Introduction to Harmonic Analysis
31
Telecommunications and Space Exploration
64
Sound Music and Computers
113
Fourier Optics and the Synchrotron Light
143
The Radon Transform and Computerized Tomography 215
214
Imaging and Spectroscopy
237
Radioastronomy and Modern Cosmology
275
Appendix
311
81
327
Index
337
116
338
124
346
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