Ole Christensen

Functions, Spaces, and Expansions (eBook, PDF)

Mathematical Tools in Physics and Engineering

• Format: PDF

Produktbeschreibung

This graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outside the field of pure mathematics. Although the treatment of each topic is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are fundamental to exploring the computational aspects of physics and engineering.

Readers are expected to have a solid understanding of linear algebra, in Rⁿ and in general vector spaces. Familiarity with the basic concepts of calculus and real analysis, including Riemann integrals and infinite series of real or complex numbers, is also required.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 266
• Erscheinungstermin: 27. Mai 2010
• Englisch
• ISBN-13: 9780817649807
• Artikelnr.: 43729499

Inhaltsangabe

Mathematical Background.- Normed Vector Spaces.- Banach Spaces.- Hilbert Spaces.- The Lp-spaces.- The Hilbert Space L2.- The Fourier Transform.- An Introduction to Wavelet Analysis.- A Closer Look at Multiresolution Analysis.- B-splines.- Special Functions.- Appendix A.- Appendix B.

Rezensionen

From the reviews:

"This textbook presents basic mathematical tools of computational harmonic analysis for students of applied mathematics, physics and engineering and presupposes only mild knowledge from linear algebra, calculus and real analysis. ... This book is carefully written and surely provides a rewarding read for the intended audience. It also contains a number of well selected exercises at the end of each chapter." (R. Steinbauer, Monatshefte für Mathematik, Vol. 169 (1), January, 2013)

"This textbook aims at representing the mathematical tools of computational harmonic and Fourier analysis in a form that is suitable for students in applied mathematics, physics and engineering. ... The book is beautifully written. It contains also a lot of suitable exercises at the end of each section." (Gerlind Plonka-Hoch, Zentralblatt MATH, Vol. 1231, 2012)

"This book is ... aimed at students of applied mathematics and engineering. ... it is clearly written and it does providea useful summary of the basic properties of the tools it covers. It does a good job of explaining the difference in the various function spaces. It has detailed coverage of wavelets and the related subjects of B-splines and multiresolution analysis, although still without applications." (Allen Stenger, The Mathematical Association of America, December, 2010)