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

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

• Publisher: Morgan & Claypool Publishers
• Year: 2019
• Tongue: English
• Leaves: 236
• Series: Synthesis Lectures on Mathematics and Statistics
• Category: Library

✦ Synopsis

This book reviews the algebraic prerequisites of calculus, including solving equations, lines, quadratics, functions, logarithms, and trig functions.

It introduces the derivative using the limit-based definition and covers the standard function library and the product, quotient, and chain rules. It explores the applications of the derivative to curve sketching and optimization and concludes with the formal definition of the limit, the squeeze theorem, and the mean value theorem.

✦ Table of Contents

Preface
Acknowledgments
Review of Algebra
Solving Equations
Lines
Computing Slopes, Finding Lines from Points
Parallel and Orthogonal Lines
Quadratic Equations
Factoring a Quadratic
Completing the Square
The Quadratic Equation
Functions
Domain and Range
The Library of Functions
Polynomials
Powers, Logs, and Exponentials
Powers and Roots
Exponentials and Logs
Trigonometric Functions
Graphs of the Basic Trig Functions
Theorems about Triangles
The Sum, Difference, and Double and Half-angle Identities
Euler's Identity
Limits, Derivatives, Rules, and the Meaning of the Derivative
Limits
Split-rule Functions
Derivatives
Derivatives of Sums and Constant Multiples
Derivatives of the Library of Functions
Logs and Exponents
The Trigonometric Functions
Inverse Trigonometric Functions
The Product, Quotient, Reciprocal, and Chain Rules
Functional Composition and the Chain Rule
Physical Interpretation of Derivatives
Implicit Derivatives
Logarithmic Differentiation
Curve Sketching
Limits at Infinity
Information from the Derivative
Increasing and Decreasing Ranges
Concavity
The Full Report for Curve Sketching
Optimization
Optimization with Derivatives
Optimization Story Problems
Limits and Continuity: The Details
Limits and Continuity
The Squeeze Theorem and the Mean Value Theorem
Useful Formulas
Powers, Logs, and Exponentials
Trigonometric Identities
Speed of Function Growth
Derivative Rules
Author's Biography
Index

✦ Subjects

Mathematics;Calculus; Elementary calculus textbooks