Introduction to Analysis

Introduction to Analysis

3.46 (32 ratings by Goodreads)
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For one/two-semester, junior/senior-level courses in Advanced Calculus, Analysis I, Real Analysis taken by math majors. The first semester is usually a general requirement; the second semester is often an option for the more motivated students.Designed to challenge advanced students while bringing weaker students up to speed, this text is an advantageous alternative to most other analysis texts which either tend to be "too easy" (designed for an Intermediate Analysis course) or "too difficult" (designed for students headed for a Ph.D. in Pure Mathematics)-both of which usually tend to slight multidimensional material. Hailed for its readability, practicality, and flexibility, this text presents the Fundamental Theorems from a very practical point of view. Introduction to Analysis starts slowly and carefully, with a focused presentation of the material; saves extreme abstraction for the second semester; provides optional enrichment sections; includes many routine exercises and examples; and liberally supports (with examples and hints) what little theory is developed in the exercises.
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Product details

  • Hardback | 611 pages
  • 184.4 x 242.3 x 27.7mm | 1,119.7g
  • Pearson
  • United States
  • English
  • 2nd edition
  • 0130144096
  • 9780130144096

Table of contents

I. ONE-DIMENSIONAL THEORY. 1. The Real Number System. 2. Sequences in R. 3. Continuity on R. 4. Differentiability on R. 5. Integrability on R. 6. Infinite Series of Real Numbers. 7. Infinite Series of Functions. II. MULTIDIMENSIONAL THEORY. 8. Euclidean Spaces. 9. Topology of Euclidean Spaces. 10. Metric Spaces. 11. Differentiability on Rn. 12. Integration on Rn. 13. Fundamental Theorems of Vector Calculus. 14. Fourier Series. 15. Differentiable Manifolds. Appendices. References. Answers and Hints to Exercises. Subject Index. Notation Index.
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32 ratings
3.46 out of 5 stars
5 16% (5)
4 38% (12)
3 28% (9)
2 16% (5)
1 3% (1)
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