Analysis Tools with Applications by Bruce K. Driver

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About this book :-
These are lecture notes are about Real analysis and Partial Differential Equations.

Book Detail :-
This book has following details information.
Title: Analysis Tools with Applications by Bruce K. Driver by NA
Publisher: Springer
Series: eBooksDirectory
Year: 2003
Pages: 790
Type: PDF
Language: English
ISBN-10 #: N\A
ISBN-13 #: N\A
Country: Pakistan
License: N\A
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About Author :-
The author NA NA

Book Contents :-
conver the following topics.
Part-I Basic Topological, Metric and Banach Space Notions 1. Limits, sums, and other basics 2. Metric, Banach and Topological Spaces 3. Locally Compact Hausdorff Spaces Part-II The Riemann Integral and Ordinary Differential Equations 4. The Riemann Integral 5. Hölder Spaces 6. Ordinary Differential Equations in a Banach Space Part-III Lebesbgue Integration Theory 7. Algebras, s — Algebras and Measurability 8. Measures and Integration 9. Fubini’s Theorem 10. Lp -spaces 11. Approximation Theorems and Convolutions 12. Construction of Measures 13. Daniell Integral Proofs Part-IV Hilbert Spaces and Spectral Theory of Compact Operators 14. Hilbert Spaces 15. Polar Decomposition of an Operator 16. Compact Operators 17. Spectral Theorem for Self-Adjoint Operators Part-V Synthesis of Integral and Differential Calculus 18. Complex Measures, Radon-Nikodym Theorem and the Dual of Lp 19. Banach Space Calculus 20. Lebesgue Di?erentiation and the Fundamental Theorem of Calculus 21. The Change of Variable Theorem 22. Surfaces, Surface Integrals and Integration by Parts Part-VI Further Hilbert and Banach Space Techniques 23. Inverse Function Theorem and Embedded Submanifolds 24. The Flow of a Vector Fields on Manifolds 25. Co-Area Formula in Riemannian Geometry 26. Application of the Co-Area Formulas 27. More Point Set Topology 28. Three Fundamental Principles of Banach Spaces 29. Weak and Strong Derivatives Part-VII Complex Variable Theory 30. Complex Di?erentiable Functions 31. Littlewood Payley Theory Part-VIII The Fourier Transform 32. Fourier Transform 33. Constant Coe?cient partial di?erential equations Part-IX Generalized Functions 34. Elementary Generalized Functions / Distribution Theory 35. Convolutions involving distributions Part-X PDE Examples 36. Some Examples of PDE’s Part-XI First Order Scalar Equations 37. First Order Quasi-Linear Scalar PDE 38. Fully nonlinear ?rst order PDE 39. Cauchy — Kovalevskaya Theorem Part-XII Elliptic ODE 40. A very short introduction to generalized functions 41. Elliptic Ordinary Di?erential Operators Part-XIII Constant Coe?cient Equations 42. Convolutions, Test Functions and Partitions of Unity 43. Poisson and Laplace’s Equation 44. Introduction to the Spectral Theorem 45. Heat Equation 46. Abstract Wave Equation 47. Wave Equation on Rn Part-XIV Sobolev Theory 48. Sobolev Spaces 49. Sobolev Inequalities Part-XV Variable Coe?cient Equations 50. 2nd order differential operators 51. Dirichlet Forms 52. Elliptic Regularity 53. Unbounded operators and quadratic forms 54. L2 — operators associated to E 55. Spectral Considerations Part-XVI Heat Kernel Properties 56. Construction of Heat Kernels by Spectral Methods 57. Nash Type Inequalities and Their Consequences 58. T. Coulhon Lecture Notes Part-XVII Heat Kernels on Vector Bundles 59. Heat Equation on Rn 60. An Abstract Version of E. Levi’s Argument 61. Statement of the Main Results 62. Proof of Theorems 61.7 and 61.10 63. Properties of ? 64. Proof of Theorem 61.4 and Corollary 61.6 65. Appendix: Gauss’ Lemma & Polar Coordinates 66. The Dirac Equation a la Roe’s Book 67. Appendix: VanVleck Determinant Properties 68. Miscellaneous 69. Remarks on Covariant Derivatives on Vector Bundles 70. Spin Bundle Stu? 71. The Case where M = Rn Part-XVIII PDE Extras 72. Higher Order Elliptic Equations 73. Abstract Evolution Equations Part-XIX Appendices A. Multinomial Theorems and Calculus Results A.1 Multinomial Theorems and Product Rules A.2 Taylor’s Theorem B. Zorn’s Lemma and the Hausdor? Maximal Principle

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