Applied Nonlinear Analysis (Dover Books on Mathematics)

Book Details:

• Publisher: Dover

• Author: Ivar Ekeland

• Language: English

• Binding: Paperback

• Edition: 1st Edition

• ISBN: 9780486453248

• Number of Pages: 518

• Dimensions: 9.2 x 6.1 x 1.1 inches

• Release Date: 17-11-2006

About The Book:

"Nonlinear Analysis" by Ivar Ekeland introduces the reader to the increasingly important field of nonlinear analysis, which has developed into an independent discipline with its own distinct methods and applications. This text offers an accessible introduction to nonlinear analysis without requiring extensive prior knowledge of linear analysis. It begins with basic concepts and gradually leads the reader to more complex applications, emphasizing clarity and practical use throughout the book.

The author emphasizes the simplicity of the concepts, directness of the proofs, and the clear applications of nonlinear analysis. The text is designed to be accessible to students who have an understanding of elementary Hilbert space theory, making it approachable even for those without a background in advanced mathematics.

The topics covered span a wide range, from very smooth functions to nonsmooth ones, from convex to nonconvex variational problems, and applications from diverse fields such as economics and mechanics. Each chapter is supplemented with background notes, helpful comments, and an extensive bibliography for further study.

Key Features:

• Introductory Level: Designed to be accessible for students with minimal prerequisites, requiring only a basic understanding of Hilbert spaces.

• Clear and Practical Applications: Focuses on real-world applications, offering immediate insight into the practical use of nonlinear analysis.

• Comprehensive Coverage: Covers a wide range of topics, including smooth and nonsmooth functions, convex and nonconvex variational problems, and applications to economics and mechanics.

• Theoretical and Practical Balance: Provides theoretical insights while keeping the content practical and directly applicable to current problems in various fields.

• Supplementary Materials: Includes background notes, comments, a bibliography, and indexes to enhance understanding and support further study.

Ideal for:

• Students: A great resource for students beginning to study nonlinear analysis, particularly in the context of Hilbert spaces.

• Researchers and Professionals: Suitable for those looking to apply nonlinear analysis in areas such as economics, mechanics, and optimization.

• Educators: A useful textbook for teaching nonlinear analysis in a manner that is both theoretical and applicable.

Conclusion:

"Nonlinear Analysis" by Ivar Ekeland offers an accessible and comprehensive introduction to nonlinear analysis, making it an essential text for students, researchers, and professionals. With its clear explanations, practical applications, and minimal prerequisites, this book serves as an excellent guide to understanding and applying the powerful methods of nonlinear analysis in real-world contexts.