For three-semester undergraduate-level courses in Calculus. This text combines traditional mainstream calculus with the most flexible approach to new ideas and calculator/computer technology. It contains superb problem sets and a fresh conceptual emphasis flavored by new technological possibilities. The Calculus II portion now has a new focus on differential equations.

1. Functions, Graphs, and Models. Functions and Mathematical Modeling. Graphs of Equations and Functions. Polynomials and Algebraic Functions. Transcendental Functions. Preview: What Is Calculus? 2. Prelude to Calculus. Tangent Lines and Slope Predictors. The Limit Concept. More about Limits. The Concept of Continuity. 3. The Derivative. 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. 4. Additional Applications of the Derivative. 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. 5. The Integral. 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. 6. Applications of the Integral. Riemann Sum Approximations. Volumes by the Method of Cross Sections. Volumes by the Method of Cylindrical Shells. Arc Length and Surface Area of Revolution. Force and Work. Centroids of Plane Regions and Curves. 7. Calculus of Transcendental Functions. Exponential and Logarithmic Functions. Indeterminate Forms and L'Hopîtal's Rule. More Indeterminate Forms. The Logarithm as an Integral. Inverse Trigonometric Functions. Hyperbolic Functions. 8. Techniques of Integration. Introduction. Integral Tables and Simple Substitutions. Integration by Parts. Trigonometric Integrals. Rational Functions and Partial Fractions. Trigonometric Substitutions. Integrals Involving Quadratic Polynomials. Improper Integrals. 9. Differential Equations. Simple Equations and Models. Slope Fields and Euler's Method. Separable Equations and Applications. Linear Equations and Applications. Population Models. Linear Second-Order Equations. Mechanical Vibrations. 10. Polar Coordinates and Parametric Curves. Analytic Geometry and the Conic Sections. Polar Coordinates. Area Computations in Polar Coordinates. Parametric Curves. Integral Computations with Parametric Curves. Conic Sections and Applications. 11. Infinite Series. Introduction. Infinite Sequences. Infinite Series and Convergence. Taylor Series and Taylor Polynomials. The Integral Test. Comparison Tests for Positive-Term Series. Alternating Series and Absolute Convergence. Power Series. Power Series Computations. Series Solutions of Differential Equations. 12. Vectors, Curves, and Surfaces in Space. Vectors in the Plane. Three-Dimensional Vectors. The Cross Product of Vectors. Lines and Planes in Space. Curves and Motions in Space. Curvature and Acceleration. Cylinders and Quadric Surfaces. Cylindrical and Spherical Coordinates. 13. Partial Differentiation. Introduction. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Multivariable Optimization Problems. Increments and Linear Approximation. The Multivariable Chain Rule. Directional Derivatives and the Gradient Vector. Lagrange Multipliers and Constrained Optimization. Critical Points of Functions of Two Variables. 14. Multiple Integrals. Double Integrals. Double Integrals over More General Regions. Area and Volume by Double Integration. Double Integrals in Polar Coordinates. Applications of Double Integrals. Triple Integrals. Integration in Cylindrical and Spherical Coordinates. Surface Area. Change of Variables in Multiple Integrals. 15. Vector Calculus. Vector Fields. Line Integrals. The Fundamental Theorem and Independence of Path. Green's Theorem. Surface Integrals. The Divergence Theorem. Stokes' Theorem. Appendices. Answers. Index.

NEW - Free CD—Shows animations of nearly all the text examples. It also has the entire book in Maple notebooks. NEW - An entire chapter devoted to calculus of transcendental functions—Combines parts of two previous chapters into the new Ch. 7. Provides students with a clearer explanation of this subject within one solid, unified, and fully rewritten chapter. NEW - Expanded treatment of differential equations (New Chapter 9). Introduces students to both direction fields and Euler's method together with the more symbolic elementary methods and applications for both first- and second-order equations. NEW - 1040 new True/False Questions—Available on the CD. They focus on theory and push the student to read. NEW - Reorganized content—Covers applied max-min problems in Ch.3 and defers related rates to Ch.4. Offers students the opportunities to focus on and study these challenging topics in separate chapters—and test their knowledge of them in separate unit tests. Approximately 7000 total problems and interesting applications—Covers all ranges of difficulty, highly theoretical and computationally oriented problems. Encourages students to learn by doing. Technology projects—Features icons that take users to Maple/ Mathematica/MATLAB/Calculator resources on the CD-ROM. Gives students the opportunity to apply conceptually based technology following key sections of the text. 320 Section-ending Concepts: Questions & Discussion. Serves students with a basis for either writing assignments or class discussion. Small optional section of matrix terminology and notation in the multivariable portion of the text. A lively and accessible writing style. Helps students feel comfortable with the topics covered, and their ability to master them. Most visual text on the market. Highlights are hundreds of Mathematica and MATLAB generated figures.

An entire chapter devoted to calculus of transcendental functions–Combines parts of two previous chapters into the new Ch. 7. Provides students with a clearer explanation of this subject within one solid, unified, and fully rewritten chapter. Expanded treatment of differential equations (New Chapter 9). Introduces students to both direction fields and Euler's method together with the more symbolic elementary methods and applications for both first- and second-order equations. Reorganized content–Covers applied max-min problems in Ch.3 and defers related rates to Ch.4. Offers students the opportunities to focus on and study these challenging topics in separate chapters–and test their knowledge of them in separate unit tests.