Franklin

Calculus Deconstructed : A Second Course in First-Year Calculus.

Author/Creator:
Nitecki, Zbigniew H.
Publication:
Washington : American Mathematical Society, 2007.
Format/Description:
Book
1 online resource (508 pages)
Series:
MAA Textbooks
MAA Textbooks
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Other records:
Subjects:
Calculus -- Textbooks.
Calculus -- Problems, exercises, etc.
Form/Genre:
Electronic books.
Contents:
cover
copyright page
title page
Preface
Contents
Precalculus
Numbers and Notation in History
Numbers, Points, and the Algebra of Inequalities
Intervals
Sequences and their Limits
Real Sequences
Limits of Real Sequences
Convergence to Unknown Limits
Finding Limits
Bounded Sets
The Bisection Algorithm (Optional)
Continuity
Continuous Functions
The Intermediate Value Theorem and Inverse Functions
Extreme Values and Bounds for Functions
Limits of Functions
Discontinuities
Exponentials and Logarithms
Epsilons and Deltas (Optional)
Differentiation
Slope, Speed and Tangents
Formal Differentiation I: The Algebra of Derivatives
Formal Differentiation II: Exponentials and Logarithms
Formal Differentiation III: Inverse Functions
Formal Differentiation IV: The Chain Rule and Implicit Differentiation
Related Rates
Extrema Revisited
Geometric Application of Limits and Derivatives
Mean Value Theorems
L'Hôpital's Rule and Indeterminate Forms
Continuity and Derivatives (Optional)
Integration
Area and the Definition of the Integral
General Theory of the Riemann Integral
The Fundamental Theorem of Calculus
Formal Integration I: Manipulation Formulas
Formal Integration II: Trigonometric Functions
Formal Integration III: Rational Functions and Partial Fractions
Improper Integrals
Geometric Applications of Riemann Sums
Riemann's Characterization of Integrable Functions (Optional)
Power Series
Local Approximation of Functions by Polynomials
Convergence of Series
Unconditional Convergence
Convergence of Power Series
Handling Power Series
Complex Numbers and Analytic Functions (Optional)
The Rhetoric of Mathematics (Methods of Proof)
Answers to Selected Problems
Bibliography
Index
About the Author.
Notes:
Description based on publisher supplied metadata and other sources.
Local notes:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2021. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Other format:
Print version: Nitecki, Zbigniew H. Calculus Deconstructed
ISBN:
9781614446026
9780883857564
OCLC:
939263619