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Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Real analysis, real variables > Elements of Real Analysis: (Dover Books on Mathematics)
Elements of Real Analysis: (Dover Books on Mathematics)

Elements of Real Analysis: (Dover Books on Mathematics)


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About the Book

Classic text explores intermediate steps between basics of calculus and ultimate stage of mathematics - abstraction and generalization. Covers fundamental concepts, real number system, point sets, functions of a real variable, Fourier series, more. Over 500 exercises.

Table of Contents:
Preface Part I. Fundamental Concepts 1. Sets and Functions 1. Sets 2. The Algebra of Sets 3. Functions 4. Countability 2. The Rational Numbers 5. Alebraic Properties 6. Decimal Expansions Part II. The Real Line 3. The Real Number System 7. Cauchy Sequences and Their Equivalence Classes 8. The Real Number System 9. Completeness Properties of R 10. The Extended Real Line 4. Sequences and Series of Number 11. Sequences: Basic Limit Theorems 12. Upper and Lower Limits 13. Basic Properties of Series 14. Series with Nonnegative Terms 15. Alternating Series 16. Absolute Convergence 5. The Structure of Point Sets 17. Basic Notions 18. Closed Sets 19. Open Sets 20. Perfect Sets 21. Distance between Point Sets 22. Connected Sets 3. Functions of a Real Variable 23. Continuity; Limits of Functions 24. Continuous Functions 25. The Nature of Discontinuities 26. Monotonic Functions 27. Uniform Continuity 7. Differentiability 28 The Derivative at a Point 29. A Continuous Nowhere Differentiable Function 30. Properties of the Derivative 31. Taylor's Theorem 8. Spaces of Continuous Functions 32. The Problems of Separability and Convergence 33. Uniform Convergence 34. Power Series 35. The Approximation of Functions 36. Equicontinuity 37. Summary 9. Measure and Integration 38. Measurable Sets 39. Properties of Measurable Sets 40. Measurable Functions 41. The Lebesgue Integral of Simple Functions 42. The Lebesgue Integral 43. Theorems on Limits under the Integral Sign 44. The Riemann Integral 10. Fourier Series 45. Basic Facts 46. The Space GBP superscript 2 47. The Question of Convergence Bibliography; Glossary of Symbols; Index


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Product Details
  • ISBN-13: 9780486653853
  • Publisher: Dover Publications Inc.
  • Publisher Imprint: Dover Publications Inc.
  • Edition: New edition
  • Language: English
  • Series Title: Dover Books on Mathematics
  • Width: 135 mm
  • ISBN-10: 0486653854
  • Publisher Date: 21 Jul 2010
  • Binding: Paperback
  • Height: 215 mm
  • Returnable: N
  • Weight: 378 gr


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