A Course in Calculus and Real Analysis

Offering a unified exposition of calculus and classical real analysis, this textbook presents a meticulous introduction to single‐variable calculus. Throughout, the exposition makes a distinction between the intrinsic geometric definition of a notion and its analytic characterization, establishing f...

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Bibliographic Details
Main Author: Ghorpade, Sudhir R. (Author)
Format: Electronic eBook
Language:English
Published: Cham : Springer International Publishing, 2018.
Edition:2nd ed. 2018.
Series:Undergraduate Texts in Mathematics,
Subjects:
Calculus.
Functions of real variables.
Sequences (Mathematics).
ISBN:9783030014001
ISSN:0172-6056
Online Access: Get full text
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Table of Contents:
  • 1. Numbers and Functions
  • 2. Sequences
  • 3. Continuity and Limits
  • 4. Differentiation
  • 5. Applications of Differentiation
  • 6. Integration
  • 7. Elementary Transcendental Functions
  • 8. Applications and Approximations of Riemann Integrals
  • 9. Infinite Series and Improper Integrals
  • 10. Sequences and Series of Functions, Integrals Depending on a Parameter
  • A. Construction of the Real Numbers
  • B. Fundamental Theorem of Algebra
  • References
  • List of Symbols and Abbreviations
  • Index.

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