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| Preface | |
| To the Student | |
| Diagnostic Tests | |
| A Preview of Calculus | |
| Functions and Models | |
| Four Ways to Represent a Function | |
| Mathematical Models: A Catalog of Essential Functions | |
| New Functions from Old Functions | |
| Graphing Calculators and Computers | |
| Exponential Functions | |
| Inverse Functions and Logarithms | |
| Parametric Curves | |
| Laboratory Project: Running Circles around Circles | |
| Review | |
| Principles of Problem Solving | |
| Limits and Derivatives | |
| The Tangent and Velocity Problems | |
| The Limit of a Function | |
| Calculating Limits Using the Limit Laws | |
| Continuity | |
| Limits Involving Infinity | |
| Derivatives and Rates of Change | |
| Writing Project: Early Methods for Finding Tangents | |
| The Derivative as a Function | |
| What Does f?? Say about f? Review | |
| Focus on Problem Solving | |
| Differentiation Rules | |
| Derivatives of Polynomials and Exponential Functions | |
| Applied Project: Building a Better Roller Coaster | |
| The Product and Quotient Rules | |
| Derivatives of Trigonometric Functions | |
| The Chain Rule | |
| Laboratory Project: BTzier Curves | |
| Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation | |
| Inverse Trigonometric Functions and their Derivatives | |
| Derivatives of Logarithmic Functions | |
| Discovery Project: Hyperbolic Functions | |
| Rates of Change in the Natural and Social Sciences | |
| Linear Approximations and Differentials | |
| Laboratory Project: Taylor Polynomials | |
| Review | |
| Focus on Problem Solving | |
| Applications of Differentiation | |
| Related Rates | |
| Maximum and Minimum Values | |
| Applied Project: The Calculus of Rainbows | |
| Derivatives and the Shapes of Curves | |
| Graphing with Calculus and Calculators | |
| Indeterminate Forms and l'Hospital's Rule | |
| Writing Project: The Origins of l'Hospital's Rule | |
| Optimization Problems | |
| Applied Project: The Shape of a Can | |
| Newton's Method | |
| Antiderivatives | |
| Review | |
| Focus on Problem Solving | |
| Integrals | |
| Areas and Distances | |
| The Definite Integral | |
| Evaluating Definite Integrals | |
| Discovery Project: Area Functions | |
| The Fundamental Theorem of Calculus | |
| Writing Project: Newton, Leibniz, and the Invention of Calculus | |
| The Substitution Rule | |
| Integration by Parts | |
| Additional Techniques of Integration | |
| Integration Using Tables and Computer Algebra Systems | |
| Discovery Project: Patterns in Integrals | |
| Approximate Integration | |
| Improper Integrals | |
| Review | |
| Focus on Problem Solving | |
| Applications of Integration | |
| More about Areas | |
| Volumes | |
| Discovery Project: Rotating on a Slant | |
| Volumes by Cylindrical Shells | |
| Arc Length | |
| Discovery Project: Arc Length Contest | |
| Average Value of a Function | |
| Applied Project: Where To Sit at the Movies | |
| Applications to Physics and Engineering | |
| Discovery Project: Complementary Coffee Cups | |
| Applications to Economics and Biology | |
| Probability | |
| Review | |
| Focus on Problem Solving | |
| Differential Equations | |
| Modeling with Differential Equations | |
| Direction Fields and Euler's Method | |
| Separable Equations | |
| Applied Project: How Fast Does a Tank Drain? Applied Project: Which Is Faster, Going Up or Coming Down? Exponential Growth and Decay | |
| Applied Project: Calculus and Baseball | |
| The Logistic Equation | |
| Predator-Prey Systems | |
| Review | |
| Focus on Problem Solving | |
| Infinte Sequences and Series | |
| Sequences | |
| Laboratory Project: Logistic Sequences | |
| Series | |
| The Integral and Comparison Tests | |
| Estimating Sums | |
| Other Convergence Tests | |
| Power Series | |
| Representations of Functions as Power Series | |
| Taylor and Maclaurin Series | |
| Laboratory Project: An Elusive Limit | |
| Writing Project: How Newton Discovered the Binomial Series | |
| Applications of Taylor Polynomials | |
| Applied Project: Radiation from the Stars | |
| Review | |
| Focus on Problem Solving | |
| Vectors and the Geometry of Space | |
| Three-Dimensional Coordinate Systems | |
| Vectors | |
| The Dot Product | |
| The Cross Product | |
| Discovery Project: The Geometry of a Tetrahedron | |
| Equations of Lines and Planes | |
| Laboratory Project: Putting 3D in Perspective | |
| Functions and Surfaces | |
| Cylindrical and Spherical Coordinates | |
| Laboratory Project: Families of Surfaces | |
| Review | |
| Focus on Problem Solving | |
| Vector Functions | |
| Vector Func | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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