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