A Course in Calculus and Real Analysis

• Main Authors: Ghorpade, Sudhir R. (Author, http://id.loc.gov/vocabulary/relators/aut), Limaye, Balmohan V. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 2nd ed. 2018.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Calculus.; Functions of real variables.; Sequences (Mathematics).; Real Functions.; Sequences, Series, Summability.

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...

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.