Polynomials, Power Series and Calculus (University Series in Undergraduate Mathematics)

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 Antiderivative
- 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