Polynomials, Power Series, and Calculus

Description

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