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

Description

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. 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