Multivariable Calculus [Paperback]

Functions and Mathematical Modeling. Graphs of Equations and Functions. Polynomials and Algebraic Functions. Transcendental Functions. Preview: What Is Calculus?

Tangent Lines and Slope Predictors. The Limit Concept. More about Limits. The Concept of Continuity.

The Derivative and Rates of Change. Basic Differentiation Rules. The Chain Rule. Derivatives of Algebraic Functions. Maxima and Minima of Functions on Closed Intervals. Applied Optimization Problems. Derivatives of Trigonometric Functions. Successive Approximations and Newton's Method.

Implicit Functions and Related Rates. Increments, Differentials, and Linear Approximation. Increasing and Decreasing Functions and the Mean Value Theorem. The First Derivative Test and Applications. Simple Curve Sketching. Higher Derivatives and Concavity. Curve Sketching and Asymptotes.

Introduction. Antiderivatives and Initial Value Problems. Elementary Area Computations. Riemann Sums and the Integral. Evaluation of Integrals. The Fundamental Theorem of Calculus. Integration by Substitution. Areas of Plane Regions. Numerical Integration.