Introduction to Analysis

Introduction to Analysis

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A textbook based on a one-semester course taught at MIT. Topics include real numbers and monotone sequences, estimations and approximations, limit theorems for sequences, local and global behavior, differentiation, the Riemann integral, infinite sets and the Lebesgue integral, and continuous functio
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Product details

  • Hardback | 460 pages
  • 182 x 238 x 28mm | 920.79g
  • Pearson
  • Upper Saddle River, NJ, United States
  • English
  • 0130811327
  • 9780130811325
  • 1,777,002

Table of contents

1. Real Numbers and Monotone Sequences. 2. Estimations and Approximations. 3. The Limit of a Sequence. 4. The Error Term. 5. Limit Theorems for Sequences. 6. The Completeness Principle. 7. Infinite Series. 8. Power Series. 9. Functions of One Variable. 10. Local and Global Behavior. 11. Continuity and Limits of Functions. 12. The Intermediate Value Theorem. 13. Continuous Functions on Compact Intervals. 14. Differentiation: Local Properties. 15. Differentiation: Global Properties. 16. Linearization and Convexity. 17. Taylor Approximation. 18. Integrability. 19. The Riemann Integral. 20. Derivatives and Integrals. 21. Improper Integrals. 22. Sequences and Series of Functions. 23. Infinite Sets and the Lebesgue Integral. 24. Continuous Functions on the Plane. 25. Point-sets in the Plane. 26. Integrals with a Parameter. 27. Differentiating Improper Integrals. Appendix. A. Sets, Numbers, and Logic. B. Quantifiers and Negation. C. Picard's Method. D. Applications to Differential Equations. E. Existence and Uniqueness of ODE Solutions.
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14 ratings
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