
- 320 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
Techniques of Functional Analysis for Differential and Integral Equations
About this book
Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given. The work provides many examples and exercises drawn from the literature.- Provides an introduction to mathematical techniques widely used in applied mathematics and needed for advanced research in ordinary and partial differential equations, integral equations, numerical analysis, fluid dynamics and other areas- Establishes the advanced background needed for sophisticated literature review and research in differential equations and integral equations- Suitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics
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Information
Table of contents
- Cover image
- Title page
- Table of Contents
- Copyright
- Preface
- Chapter 1: Some Basic Discussion of Differential and Integral Equations
- Chapter 2: Vector Spaces
- Chapter 3: Metric Spaces
- Chapter 4: Banach Spaces
- Chapter 5: Hilbert Spaces
- Chapter 6: Distribution Spaces
- Chapter 7: Fourier Analysis
- Chapter 8: Distributions and Differential Equations
- Chapter 9: Linear Operators
- Chapter 10: Unbounded Operators
- Chapter 11: Spectrum of an Operator
- Chapter 12: Compact Operators
- Chapter 13: Spectra and Green’s Functions for Differential Operators
- Chapter 14: Further Study of Integral Equations
- Chapter 15: Variational Methods
- Chapter 16: Weak Solutions of Partial Differential Equations
- Appendix
- Bibliography
- Index