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.
Ausstattung/Bilder: 2011. 742 S. w. 80 ill. 247 mm
Abmessung: 246mm x 177mm x 40mm
'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-Universitat Marburg
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 in the Netherlands.
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.
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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