Table of Contents
(Each chapter ends with Key Terms and Review Exercises.)
Prerequisites for Calculus.
Lines.
Functions and Graphs.
Exponential Functions.
Parametric Equations.
Functions and Logarithms.
Trigonometric Functions.
Limits and Continuity. Rates of Change and Limits.
Limits Involving Infinity.
Continuity.
Rates of Change and Tangent Lines.
Derivatives. Derivative of a Function.
Differentiability.
Rules for Differentiation.
Velocity and Other Rates of Change.
Derivatives of Trigonometric Functions.
Chain Rule.
Implicit Differentiation.
Derivatives of Inverse Trigonometric Functions.
Derivatives of Exponential and Logarithmic Functions.
Calculus at Work.
Applications of Derivatives. Extreme Values of Functions.
Mean Value Theorem.
Connecting f' and f' with the Graph of f.
Modeling and Optimization.
Linearization and Newton's Method.
Related Rates.
The Definite Integral. Estimating with Finite Sums.
Definite Integrals.
Definite Integrals and Antiderivatives.
Fundamental Theorem of Calculus.
Trapezoidal Rule.
Key Terms.
Calculus At Work.
Differential Equations and Mathematical Modeling. Antiderivatives and Slope Fields.
Integration by Substitution.
Integration by Parts.
Exponential Growth andDecay.
Population Growth.
Numerical Methods.
Calculus At Work.
Applications of Definite Integrals. Integral as Net Change.
Areas in the Plane.
Volumes.
Lengths of Curves.
Applications from Science and Statistics.
Calculus at Work.
L'Hôpital's Rule, Improper Integrals, and Partial Fractions. L'Hôpital's Rule.
Relative Rates of Growth.
Improper Integrals.
Partial Fractions and Integral Tables.
Infinite Series. Power Series.
Taylor Series.
Taylor's Theorem.
Radius of Convergence.
Testing Convergence at Endpoints.
Calculus at Work.
Parametric, Vector, and Polar Functions. Parametric Functions.
Vectors in the Plane.
Vector-valued Functions.
Modeling Projectile Motion.
Polar Coordinates and Polar Graphs.
Calculus of Polar Curves.
Cumulative Review. Appendices. Formulas from Precalculus Mathematics.
Mathematical Induction.
Using the Limit Definition.
Proof of the Chain Rule.
Conic Sections.
Hyperbolic Functions.
Brief Table of Integrals.
Glossary. Selected Answers/Solutions. Applications Index. Index.
