1. Functions 1.1 Functions and Their Graphs 1.2 Combining Functions; Shifting and Scaling Graphs 1.3 Trigonometric Functions 1.4 Graphing with Software 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms   2. Limits and Continuity 2.1 Rates of Change and Tangents to Curves 2.2 Limit of a Function and Limit Laws 2.3 The Precise Definition of a Limit 2.4 One-Sided Limits 2.5 Continuity 2.6 Limits Involving Infinity; Asymptotes of Graphs   3. Derivatives 3.1 Tangents and the Derivative at a Point 3.2 The Derivative as a Function 3.3 Differentiation Rules 3.4 The Derivative as a Rate of Change 3.5 Derivatives of Trigonometric Functions 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Inverse Functions and Logarithms 3.9 Inverse Trigonometric Functions 3.10 Related Rates 3.11 Linearization and Differentials   4. Applications of Derivatives 4.1 Extreme Values of Functions 4.2 The Mean Value Theorem 4.3 Monotonic Functions and the First Derivative Test 4.4 Concavity and Curve Sketching 4.5 Indeterminate Forms and L’Hôpital’s Rule 4.6 Applied Optimization 4.7 Newton's Method 4.8 Antiderivatives   5. Integration 5.1 Area and Estimating with Finite Sums 5.2 Sigma Notation and Limits of Finite Sums 5.3 The Definite Integral 5.4 The Fundamental Theorem of Calculus 5.5 Indefinite Integrals and the Substitution Method 5.6 Substitution and Area Between Curves   6. Applications of Definite Integrals 6.1 Volumes Using Cross-Sections 6.2 Volumes Using Cylindrical Shells 6.3 Arc Length 6.4 Areas of Surfaces of Revolution 6.5 Work and Fluid Forces 6.6 Moments and Centers of Mass   7. Integrals and Transcendental Functions 7.1 The Logarithm Defined as an Integral 7.2 Exponential Change and Separable Differential Equations 7.3 Hyperbolic Functions 7.4 Relative Rates of Growth   8. Techniques of Integration 8.1 Using Basic Integration Formulas 8.2 Integration by Parts 8.3 Trigonometric Integrals 8.4 Trigonometric Substitutions 8.5 Integration of Rational Functions by Partial Fractions 8.6 Integral Tables and Computer Algebra Systems 8.7 Numerical Integration 8.8 Improper Integrals 8.9 Probability   9. First-Order Differential Equations 9.1 Solutions, Slope Fields, and Euler's Method 9.2 First-Order Linear Equations 9.3 Applications 9.4 Graphical Solutions of Autonomous Equations 9.5 Systems of Equations and Phase Planes   10. Infinite Sequences and Series 10.1 Sequences 10.2 Infinite Series 10.3 The Integral Test 10.4 Comparison Tests 10.5 Absolute Convergence; The Ratio and Root Tests 10.6 Alternating Series and Conditional Convergence 10.7 Power Series 10.8 Taylor and Maclaurin Series 10.9 Convergence of Taylor Series 10.10 The Binomial Series and Applications of Taylor Series   11. Parametric Equations and Polar Coordinates 11.1 Parametrizations of Plane Curves 11.2 Calculus with Parametric Curves 11.3 Polar Coordinates 11.4 Graphing Polar Coordinate Equations 11.5 Areas and Lengths in Polar Coordinates 11.6 Conic Sections 11.7 Conics in Polar Coordinates

Strong exercise sets feature a great breadth of problems–progressing from skills problems to applied and theoretical problems–to encourage students to think about and practice the concepts until they achieve mastery. Figures are conceived and rendered to provide insight for students and support conceptual reasoning. The flexible table of contents divides topics into manageable sections, allowing instructors to tailor their course to meet the specific needs of their students. Complete and precise multivariable coverage enhances the connections of multivariable ideas with their single-variable analogues studied earlier in the book. A robust MyMathLab course contains nearly 9,000 assignable exercises, a complete eBook, and built-in tutorials so students can get help whenever they need it. A complete suite of instructor and student supplements saves class preparation time for instructors and improves students’ learning.  

Two new sections: Section 8.1 reviews basic integration formulas and the Substitution Rules combined with algebraic methods and trigonometric identities Section 8.10 on probability as an application of improper integrals to making predictions for probabilistic models, with a wide range of applications in business and sciences Presentation of absolute convergence before considering the Ratio and Root Tests for convergence of a series, which allows the tests to be stated in their stronger forms (Theorems 13 and 14, Section 10.5) MyMathLab now has hundreds of additional assignable exercises, including 670 that address prerequisite skills, giving you the selection you need to create the right homework assignments and assessments. Updated and new art, and additional tables, supporting examples and exercises throughout Material has been rewritten or enhanced, for greater clarity or improved motivation. Here are some examples:   Definition of continuous at x = c Geometric insight into L’Hôpital’s Rule Discussion of cycloid curve Most chapter introductory overviews A variety of new examples throughout, including: Predicting the rise in college tuition costs Predicting the decline in tuberculosis death rates Minimizing production costs Integration by parts Log formula for the inverse hyperbolic sine function Using the Integral Test Finding the perimeter of an ellipse Updated and new exercises, including: Using regression analysis to predict Federal minimum wage, median home and energy prices, and global warming More limits involving rational functions Interpreting derivatives from graphs Growth in the Gross National Product Vehicular stopping distance Spread of an oil spill in gulf waters Estimating concentration of a drug Considering endangered species Prescribing drug dosage Summing infinitely many areas Representing functions by a geometric series Unusual polar graphs Finding the distance between skew lines in space Finding mass and distances in our solar system