Andrea Prosperetti

Advanced Mathematics for Applications (eBook, PDF)

• Format: PDF

Produktbeschreibung

The partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working physical scientist and engineer. Andrea Prosperetti draws on many years' research experience to produce a guide to a wide variety of methods, ranging from classical Fourier-type series through to the theory of distributions and basic functional analysis. Theorems are stated precisely and their meaning explained, though proofs are mostly only sketched, with comments and examples being given more prominence. The book structure does not require sequential reading: each chapter is self-contained and users can fashion their own path through the material. Topics are first introduced in the context of applications, and later complemented by a more thorough presentation.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 6. Januar 2011
• Englisch
• ISBN-13: 9780511911323
• Artikelnr.: 38206841

Autorenporträt

Andrea Prosperetti is the Charles A. Miller, Jr Professor in the Department of Mechanical Engineering at The Johns Hopkins University. He also holds the Berkhoff Chair in the Department of Applied Sciences at the University of Twente, Enschede, Netherlands.

Inhaltsangabe

Preface
To the reader
List of tables
Part I. General Remarks and Basic Concepts: 1. The classical field equations
2. Some simple preliminaries
Part II. Applications: 3. Fourier series: applications
4. Fourier transform: applications
5. Laplace transform: applications
6. Cylindrical systems
7. Spherical systems
Part III. Essential Tools: 8. Sequences and series
9. Fourier series: theory
10. The Fourier and Hankel transforms
11. The Laplace transform
12. The Bessel equation
13. The Legendre equation
14. Spherical harmonics
15. Green's functions: ordinary differential equations
16. Green's functions: partial differential equations
17. Analytic functions
18. Matrices and finite-dimensional linear spaces
Part IV. Some Advanced Tools: 19. Infinite-dimensional spaces
20. Theory of distributions
21. Linear operators in infinite-dimensional spaces
Appendix
References
Index.

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Preface; To the reader; List of tables; Part I. General Remarks and Basic Concepts: 1. The classical field equations; 2. Some simple preliminaries; Part II. Applications: 3. Fourier series: applications; 4. Fourier transform: applications; 5. Laplace transform: applications; 6. Cylindrical systems; 7. Spherical systems; Part III. Essential Tools: 8. Sequences and series; 9. Fourier series: theory; 10. The Fourier and Hankel transforms; 11. The Laplace transform; 12. The Bessel equation; 13. The Legendre equation; 14. Spherical harmonics; 15. Green's functions: ordinary differential equations; 16. Green's functions: partial differential equations; 17. Analytic functions; 18. Matrices and finite-dimensional linear spaces; Part IV. Some Advanced Tools: 19. Infinite-dimensional spaces; 20. Theory of distributions; 21. Linear operators in infinite-dimensional spaces; Appendix; References; Index.

Rezensionen

'This carefully written book by a well-known expert in the area is also an excellent guide to the present literature, recommended as well to graduate students as to experts in the area. This volume will help the reader in getting acquainted with some mathematical aspects of the modern theory of linear and non-linear phenomena arising in relevant applications to mathematical physics.' Zentralblatt MATH