Functions, spaces, and expansions: mathematical tools in physics and engineering

This graduate-level textbook presents a detailed exposition of key mathematical tools in analysis, which will appeal to students and professionals across science and engineering. Every topic covered has been specifically chosen because it plays a role outside the field of pure mathematics, so although the treatment of each is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are quite useful when exploring the computational areas of physics and engineering. A central theme of the textbook is the structure of various vector spaces (most importantly, Hilbert spaces) and expansions of elements in these spaces in terms of bases. As a textbookthat provides a deep understanding of central issues in mathematical analysis, Functions, Spaces, and Expansions is intended for graduate students, researchers, and practitioners in applied mathematics, physics, and engineering. Readers are expected to have a solid understanding of linear algebra, in Rn and ingeneral vector spaces. Collected topics represent a wide foundation of applied mathematical tools not often found together in one book Interdisciplinary approach provides students the mathematical tools required for studying computational topics in engineering and physics Contains over 150 exercises Presents asmooth introduction to the idea of the mathematical proof For a wide audience, including graduate students, researchers, and practitioners in mathematics, physics, and engineering INDICE: Preface.- Prologue.- Mathematical Background.- Normed Vector Spaces.- Banach Spaces.- Hilbert Spaces.- The L^p-spaces.- The Hilbert Space L^2.- The Fourier Transform.- An Introduction to Wavelet Analysis.- A Closer Look onMultiresolution Analysis.- B-splines.- Special Functions.- Appendix.- List ofSymbols.- References.- Index.

• ISBN: 978-0-8176-4979-1
• Editorial: Birkhaüser
• Encuadernacion: Rústica
• Páginas: 266
• Fecha Publicación: 01/03/2010
• Nº Volúmenes: 1
• Idioma: Inglés