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

✍ Scribed by Daniel Ashlock, Steven G. Krantz (editor)

• Publisher: Morgan & Claypool Publishers
• Year: 2019
• Tongue: English
• Leaves: 205
• Series: Synthesis Lectures on Mathematics and Statistics
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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

✦ Subjects

Mathematics;Calculus; Elementary calculus textbooks