الرياضيات التطبيقية كتاب An Introduction to Partial Differential Equations

المصدر: كتاب An Introduction to Partial Differential Equations
في منتدى : قسم الرياضيات

An Introduction to Partial Differential Equations



Book Detail:

Published May 2005
Price $250
ISBN-13: 9780521848862
Yehuda Pinchover
Technion - Israel Institute of Technology, Haifa
Jacob Rubinstein
Indiana University

Book Description:

A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, physics and engineering. The presentation is lively and up to date, paying particular emphasis to developing an appreciation of underlying mathematical theory. Beginning with basic definitions, properties and derivations of some basic equations of mathematical physics from basic principles, the book studies first order equations, classification of second order equations, and the one-dimensional wave equation. Two chapters are devoted to the separation of variables, whilst others concentrate on a wide range of topics including elliptic theory, Green’s functions, variational and numerical methods. A rich collection of worked examples and exercises accompany the text, along with a large number of illustrations and graphs to provide insight into the numerical examples. Solutions to selected exercises are included for students whilst extended solution sets are available to lecturers from solutions@cambridge.org.

Contents:

1. Introduction; 2. First-order equations; 3. Second-order linear equations; 4. The 1D wave equation; 5. Separation of variables; 6. Sturm-Liouville problem; 7. Elliptic equations; 8. Green’s function and integral representation; 9. Equations in high dimensions; 10. Variational methods; 11. Numerical methods; 12. Solutions of odd-numbered problems.

Reviews:

‘Their book spans both introductory and advanced material, making it suitable for use right through a UK undergraduate degree. … It stresses the practical applications of rigour, introduced with a touch sufficiently light not to put off the average student.‘ Times Higher Education Supplement

'The theoretical parts of the book are complemented by a good range of examples and problems. In summary, the book is a good introduction to the field that can be recommended for either class use or self-study.'
Zeitschrift für Angewandte Mathematik und Mechanik



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