Advanced mathematics for applications / Andrea Prosperetti.

Machine generated contents note: 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.

Includes bibliographical references and index.

Part 0. General remarks and basic concepts: 1. The classical field equations -- 2. Some simple preliminaries -- Part I. Applications: 3. Fourier series : applications; 4. Fourier transform : applications -- 5. Laplace transform : applications -- 6. Cylindrical systems -- 7. Spherical systems -- Part II. 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 III. Some advanced tools: 19. Infinite-dimensional spaces -- 20. Theory of distributions -- 21. Linear operators in infinite-dimensional spaces.

"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 rominence. The book structure does not require sequential reading: each chapter is elf-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"--Provided by publisher.