A Passage to Modern Analysis
eBook - PDF

A Passage to Modern Analysis

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

A Passage to Modern Analysis

About this book

A Passage to Modern Analysis is an extremely well-written and reader-friendly invitation to real analysis. An introductory text for students of mathematics and its applications at the advanced undergraduate and beginning graduate level, it strikes an especially good balance between depth of coverage and accessible exposition. The examples, problems, and exposition open up a student's intuition but still provide coverage of deep areas of real analysis. A yearlong course from this text provides a solid foundation for further study or application of real analysis at the graduate level.A Passage to Modern Analysis is grounded solidly in the analysis of $\mathbf{R}$ and $\mathbf{R}^{n}$, but at appropriate points it introduces and discusses the more general settings of inner product spaces, normed spaces, and metric spaces. The last five chapters offer a bridge to fundamental topics in advanced areas such as ordinary differential equations, Fourier series and partial differential equations, Lebesgue measure and the Lebesgue integral, and Hilbert space. Thus, the book introduces interesting and useful developments beyond Euclidean space where the concepts of analysis play important roles, and it prepares readers for further study of those developments.

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Yes, you can access A Passage to Modern Analysis by William J. Terrell in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title page
  3. List of Figures
  4. Preface
  5. Chapter 1. Sets and Functions
  6. Chapter 2. The Complete Ordered Field of Real Numbers
  7. Chapter 3. Basic Theory of Series
  8. Chapter 4. Basic Topology, Limits, and Continuity
  9. Chapter 5. The Derivative
  10. Chapter 6. The Riemann Integral
  11. Chapter 7. Sequences and Series of Functions
  12. Chapter 8. The Metric Space 𝑅ⁿ
  13. Chapter 9. Metric Spaces and Completeness
  14. Chapter 10. Differentiation in 𝑅ⁿ
  15. Chapter 11. The Inverse and Implicit Function Theorems
  16. Chapter 12. The Riemann Integral in Euclidean Space
  17. Chapter 13. Transformation of Integrals
  18. Chapter 14. Ordinary Differential Equations
  19. Chapter 15. The Dirichlet Problem and Fourier Series
  20. Chapter 16. Measure Theory and Lebesgue Measure
  21. Chapter 17. The Lebesgue Integral
  22. Chapter 18. Inner Product Spaces and Fourier Series
  23. Appendix A. The Schroeder-Bernstein Theorem
  24. Appendix B. Symbols and Notations
  25. Bibliography
  26. Index
  27. Back Cover