Product Description

This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained. The book is divided into eight parts: The first covers finite- dimensional vector spaces and the linear operators defined on them. The second is devoted to infinite-dimensional vector spaces, and includes discussions of the classical orthogonal polynomials and of Fourier series and transforms. The third part deals with complex analysis, including complex series and their convergence, the calculus of residues, multivalued functions, and analytic continuation. Part IV treats ordinary differential equations, concentrating on second-order equations and discussing both analytical and numerical methods of solution. The next part deals with operator theory, focusing on integral and Sturm--Liouville operators. Part VI is devoted to Green's functions, both for ordinary differential equations and in multidimensional spaces. Parts VII and VIII contain a thorough discussion of differential geometry and Lie groups and their applications, concluding with Noether's theorem on the relationship between symmetries and conservation laws. Intended for advanced undergraduates or beginning graduate students, this comprehensive guide should also prove useful as a refresher or reference for physicists and applied mathematicians. Over 300 worked-out examples and more than 800 problems provide valuable learning aids.

Product Details

• Amazon Sales Rank: #768512 in Books
• Published on: 2002-02-01
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 1046 pages

Customer Reviews

A very good book
In my opinion, this book is superb. I like it very much. It covers a lot of essencial topics in a very clear way, well organized, with graphics, lots of examples and problems for self-studying. It has also some historical data about the mathematicians who developed the theory, a good way to make all this abstract information more human. I strongly recommend it.

A great book!!
This book is great! It's very clear, with lots of examples and also problems to apply your knowledge. It's organitzation is superb. It covers a wide variety of topics, all of them of great importance for anyone who wants to reach a good level of mathematics applied to science. I would consider it as a must.