Thomas' Calculus Early Transcendentals

9780321198006

032119800X

(Practice Exercises, Additional Exercises, and Questions to Guide Your Review appear at the end of each chapter.) 1. Functions Functions and Their Graphs Identifying Functions; Mathematical Models Combining Functions; Shifting and Scaling Graphs Graphing with Calculators and Computers Exponential Functions Inverse Functions and Logarithms 2. Limits and Continuity Rates of Change and Limits Calculating Limits Using the Limit Laws Precise Definition of a Limit One-Sided Limits and Limits at Infinity Infinite Limits and Vertical Asymptotes Continuity Tangents and Derivatives 3. Differentiation The Derivative as a Function Differentiation Rules for Polynomials, Exponentials, Products and Quotients The Derivative as a Rate of Change Derivatives of Trigonometric Functions The Chain Rule and Parametric Equations Implicit Differentiation Derivatives of Inverse Functions and Logarithms Inverse Trigonometric Functions Related Rates Linearization and Differentials 4. Applications of Derivatives Extreme Values of Functions The Mean Value Theorem Monotonic Functions and the First Derivative Test Concavity and Curve Sketching Applied Optimization Problems Indeterminate Forms and L'Hopital's Rule Newton's Method Antiderivatives 5. Integration Estimating with Finite Sums Sigma Notation and Limits of Finite Sums The Definite Integral The Fundamental Theorem of Calculus Indefinite Integrals and the Substitution Rule Substitution and Area Between Curves 6. Applications of Definite Integrals Volumes by Slicing and Rotation About an Axis Volumes by Cylindrical Shells Lengths of Plane Curves Moments and Centers of Mass Areas of Surfaces of Revolution and The Theorems of Pappus Work &