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Elements of Real Analysis (87 Edition)by David A. Sprecher
Synopses & ReviewsPublisher Comments:This classic text in introductory analysis delineates and explores the intermediate steps between the basics of calculus and the ultimate stage of mathematics: abstraction and generalization. Since many abstractions and generalizations originate with the real line, the author has made it the unifying theme of the text, constructing the real number system from the point of view of a Cauchy sequence (a step which Dr. Sprecher feels is essential to learn what the real number system is). The material covered in Elements of Real Analysis should be accessible to those who have completed a course in calculus. To help give students a sound footing, Part One of the text reviews the fundamental concepts of sets and functions and the rational numbers. Part Two explores the real line in terms of the real number system, sequences and series of number and the structure of point sets. Part Three examines the functions of a real variable in terms of continuity, differentiability, spaces of continuous functions, measure and integration, and the Fourier series. An especially valuable feature of the book is the exercises which follow each section. There are over five hundred, ranging from the simple to the highly difficult, each focusing on a concept previously introduced. Synopsis:Classic text covers fundamental concepts, real number system, point sets, functions of a real variable, Fourier series, much more. Over 500 exercises.
Synopsis: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. Synopsis:Classic text delineates and explores intermediate steps between basics of calculus and ultimate stage of mathematics — abstraction and generalization. Examines sets and functions, rational numbers, the real line in terms of the real number system, sequences and functions of a real variable in terms of continuity, differentiability, 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 £ superscript 2 47. The Question of Convergence Bibliography; Glossary of Symbols; Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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