Polynomials, Power Series, and Calculus

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