An Introduction to Nonlinear Analysis
An Introduction to Nonlinear Analysis
The techniques that can be used to solve non-linear problems are far different than those that are used to solve linear problems. Many courses in analysis and applied mathematics attack linear cases simply because they are easier to solve and do not require a large theoretical background in order to approach them. Professor Schechter's 2005 book is devoted to non-linear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving non-linear problems is developed whilst demonstrating their application to problems in one dimension and then leading to higher dimensions. The reader is guided using simple exposition and proof, assuming a minimal set of pre-requisites. For completion, a set of appendices covering essential basics in functional analysis and metric spaces is included, making this ideal as an accompanying text on an upper-undergraduate or graduate course, or even for self-study.
- Simple exposition and easy proofs make this ideal as an accompanying text or for self study
- Provides the reader with an understanding on non-linear tools whilst deriving all proofs from first principles
- Background material is collected in four appendices
Reviews & endorsements
“This is an attractive introductory text to non-linear analysis for well-prepared and diligent students.”
UK Nonlinear News
"The possible uses of this book are numerous: a text for a graduate or upper-level undergraduate course, a self-study book, a reference book to be used when needed. The purpose of the book is to teach the methods that can be used in solving nonlinear problems, using as little background material as possible and only the simplest linear techniques...this is a book about difficult problems, with most of the background included in its appendices. It is presented in a very readable and accessible way, which makes it a perfect candidate for a textbook and a very good addition to any analyst's library."
MAA Reviews
"In general, I find the style pleasant and highly readable. There are good sets of exercises...This would make quite a nice book for a course."
E. Norman Dancer, University of Sydney, SIAM Review
Product details
September 2012Paperback
9780521605137
382 pages
229 × 152 × 22 mm
0.56kg
Available
Table of Contents
- 1. Extrema
- 2. Critical points
- 3. Boundary value problems
- 4. Saddle points
- 5. Calculus of variations
- 6. Degree theory
- 7. Conditional extrema
- 8. Minimax methods
- 9. Jumping nonlinearities
- 10. Higher dimensions.
