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.
1. Cover image - p. iv 2. Title page - p. iv 3. Table of Contents - p. iv 4. Copyright - p. iv 5. Preface - p. ix 6. Chapter 1: Some Basic Discussion of Differential and Integral Equations - p. x 7. Chapter 2: Vector Spaces - p. 27 8. Chapter 3: Metric Spaces - p. 34 9. Chapter 4: Banach Spaces - p. 50 10. Chapter 5: Hilbert Spaces - p. 58 11. Chapter 6: Distribution Spaces - p. 73 12. Chapter 7: Fourier Analysis - p. 94 13. Abstract - p. 95 14. 7.1 Fourier Series in One Space Dimension - p. 95 15. 7.2 Alternative Forms of Fourier Series - p. 100 16. 7.3 More About Convergence of Fourier Series - p. 101 17. 7.4 The Fourier Transform on RN - p. 104 18. 7.5 Further Properties of the Fourier Transform - p. 107 19. 7.6 Fourier Series of Distributions - p. 111 20. 7.7 Fourier Transforms of Distributions - p. 114 21. Chapter 8: Distributions and Differential Equations - p. 123 22. Chapter 9: Linear Operators - p. 139 23. Chapter 10: Unbounded Operators - p. 158 24. Chapter 11: Spectrum of an Operator - p. 169 25. Chapter 12: Compact Operators - p. 181 26. Chapter 13: Spectra and Green’s Functions for Differential Operators - p. 203 27. Chapter 14: Further Study of Integral Equations - p. 225 28. Chapter 15: Variational Methods - p. 241 29. Chapter 16: Weak Solutions of Partial Differential Equations - p. 267 30. Appendix - p. 295 31. Bibliography - p. 305 32. Index - p. 307
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.
1. Cover image - p. iv 2. Title page - p. iv 3. Table of Contents - p. iv 4. Copyright - p. iv 5. Preface - p. ix 6. Chapter 1: Some Basic Discussion of Differential and Integral Equations - p. x 7. Chapter 2: Vector Spaces - p. 27 8. Chapter 3: Metric Spaces - p. 34 9. Chapter 4: Banach Spaces - p. 50 10. Chapter 5: Hilbert Spaces - p. 58 11. Chapter 6: Distribution Spaces - p. 73 12. Chapter 7: Fourier Analysis - p. 94 13. Abstract - p. 95 14. 7.1 Fourier Series in One Space Dimension - p. 95 15. 7.2 Alternative Forms of Fourier Series - p. 100 16. 7.3 More About Convergence of Fourier Series - p. 101 17. 7.4 The Fourier Transform on RN - p. 104 18. 7.5 Further Properties of the Fourier Transform - p. 107 19. 7.6 Fourier Series of Distributions - p. 111 20. 7.7 Fourier Transforms of Distributions - p. 114 21. Chapter 8: Distributions and Differential Equations - p. 123 22. Chapter 9: Linear Operators - p. 139 23. Chapter 10: Unbounded Operators - p. 158 24. Chapter 11: Spectrum of an Operator - p. 169 25. Chapter 12: Compact Operators - p. 181 26. Chapter 13: Spectra and Green’s Functions for Differential Operators - p. 203 27. Chapter 14: Further Study of Integral Equations - p. 225 28. Chapter 15: Variational Methods - p. 241 29. Chapter 16: Weak Solutions of Partial Differential Equations - p. 267 30. Appendix - p. 295 31. Bibliography - p. 305 32. Index - p. 307
