Fast Start Integral Calculus (Synthesis Lectures on Mathematics and Statistics)

Description

This book introduces integrals, the fundamental theorem of calculus, initial value problems, and Riemann sums. It introduces properties of polynomials, including roots and multiplicity, and uses them as a framework for introducing additional calculus concepts including Newton's method, L'Hôpital's Rule, and Rolle's theorem. Both the differential and integral calculus of parametric, polar, and vector functions are introduced. The book concludes with a survey of methods of integration, including u-substitution, integration by parts, special trigonometric integrals, trigonometric substitution, and partial fractions. Preface Acknowledgments Integration, Area, and Initial Value Problems Anti-derivatives The Fundamental Theorem Even and Odd Functions Initial Value Problems Induction and Sums of Rectangles Parametric, Polar, and Vector Functions Parametric Functions The Derivative of a Parametric Curve Polar Coordinates Polar Calculus Vector Functions Calculus with Vector Curves The Arithmetic, Geometry, and Calculus of Polynomials Polynomial Arithmetic Qualitative Properties of Polynomials Multiplicity of Roots L'Hôpital's Rule; Strange Polynomials Strange Polynomials Methods of Integration I u-Substitution Substitution in Definite Integrals Integration by Parts Integrating Trig Functions Methods of Integration II Trigonometric Substitution Partial Fractions Practicing Integration Useful Formulas Powers, Logs, and Exponentials Trigonometric Identities Speed of Function Growth Derivative Rules Vector Arithmetic Polar and Rectangular Conversion Integral Rules Author's Biography Index