- #1
- 22,089
- 3,296
- Author: Kenneth Ross
- Title: Elementary Analysis: The Theory of Calculus
- Amazon link: https://www.amazon.com/dp/1441928111/?tag=pfamazon01-20
- Prerequisities: Proofs, Calculus
- Level: Undergrad
Table of Contents:
Code:
[LIST]
[*] Preface
[*] Introduction
[LIST]
[*] The Set N of Natural Numbers
[*] The Set Q of Rational Numbers
[*] The Set R of Real Numbers
[*] The Completeness Axiom
[*] The Symbols +\infty and -\infty
[*] A Development of R
[/LIST]
[*] Sequences
[LIST]
[*] Limits of Sequences
[*] A Discussion about Proofs
[*] Limit Theorems for Sequences
[*] Monotone Sequences and Cauchy Sequences
[*] Subsequences
[*] lim sup's and lim inf's
[*] Some Topological Concepts in Metric Spaces
[*] Series
[*] Alternating Series and Integral Tests
[*] Decimal Expansions of Real Numbers
[/LIST]
[*] Continuity
[LIST]
[*] Continuous Functions
[*] Properties of Continuous Functions
[*] Uniform Continuity
[*] Limits of Functions
[*] More on Metric Spaces: Continuity
[*] More on Metric Spaces: Connectedness
[/LIST]
[*] Sequences and Series of Functions
[LIST]
[*] Power Series
[*] Uniform Convergence
[*] More on Uniform Convergence
[*] Differentiation and Integration of Power Series
[*] Weierstrass's Approximation Theorem
[*] Differentiation
[*] Basic Properties of the Derivative
[*] The Mean Value Theorem
[*] L'Hospital's Rule
[*] Taylor's Theorem
[/LIST]
[*] Integration
[LIST]
[*] The Riemann Integral
[*] Properties of the Riemann Integral
[*] Fundamental Theorem of Calculus
[*] Riemann-Stieltjes Integrals
[*] Improper Integrals
[*] A Discussion of Exponents and Logarithms
[/LIST]
[*] Appendix on Set Notation
[*] Selected Hints and Answers
[*] References
[*] Symbols Index
[*] Index
[/LIST]
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