Polynomials, Power Series, and Calculus

✍ Scribed by Howard Levi

• Publisher: Van Nostrand
• Year: 1968
• Tongue: English
• Leaves: 167
• Series: The University Series in Undergraduate Mathematics
• Category: Library

✦ Table of Contents

Cover
Copyright
Preface
Contents
1. Background Material
Order and Absolute Values
Functions and Function Notation
Sequences
Some Polynomial Algebra
2. Polynomials
Polynomial Functions
Arithmetic Sequences and Polynomial Functions
The Algebra of Residues
Composition, Inverses, and the Extraction of Roots in Rn[x]
3. Functions Having Polynomial Approximations
Orders of Magnitude
Approximation by Polynomials
Continuous Functions
Derivatives
4. Applications Of The Derivative And Antideriv A Tive
Tangents: Maxima and Minima
Some Useful Theorems
Applications of the Antiderivative
Applications of the Derivative
Higher Derivatives; Taylor's Theorem
5. Infinite Sequences And Infinite Series
Convergence of Infinite Sequences
Cauchy Sequences
Infinite Series
Algebra of Power Series
6. Functions Defined By Power Series
Interval of Convergence
Analytic Functions
The Method of Undetermined Coefficients
7. Series Expansions Of The Elementary Functions
The Exponential Functions
Logarithms; the Binomial Theorem
Trigonometric Functions
Inverse Trigonometric Functions
Angle Measure and the Trigonometric Functions of Angles
Curvature and the Osculating Circle
Appendices
A. Some Peculiarities of Infinite Series
B. Other Notations for the Derivative and Differential
C. The Riemann Integral
Answers To Selected Exercises
Index