Advanced Mathematics for Applications
1st Edition
Published on 1. December 2010
978-0-511-91132-3 (ISBN)
Description
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.
Reviews / Votes
'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 'A truly wonderful book ... The author succeeded in creating a new type of book, that many will put on their desks, and they should: beginners, physicists, advanced learners, instructors, users of maths in the sciences ... A modern work, showing new ways, unusually multi-layered, applicable in many contexts and at many levels, an exciting book.' Siegfried Grossmann, Philipps-Universitaet Marburg 'This book admirably lays down physical and mathematical groundwork, provides motivating examples, gives access to the relevant deep mathematics, and unifies components of many mathematical areas. This sophisticated topics text, which interweaves and connects subjects in a meaningful way, gives readers the satisfaction and the pleasure of putting two and two together.' Laura K. Gross, SIAM ReviewMore details
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 20 Halftones, black and white; 60 Line drawings, black and white
File size
5,13 MB
ISBN-13
978-0-511-91132-3 (9780511911323)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Andrea Prosperetti
Advanced Mathematics for Applications
Book
01/2011
Cambridge University Press
€241.20
Shipment within 15-20 days
Andrea Prosperetti
Advanced Mathematics for Applications
Book
01/2011
Cambridge University Press
€82.00
Shipment within 15-20 days
Person
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.
Content
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.
