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| Review and Preview | |
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| Functions and Their Graphs | |
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| Types of Functions | |
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| Shifting and Scaling | |
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| Graphing Calculators and Computers | |
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| Principles of Problem Solving | |
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| A Preview of Calculus | |
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| Introduction to Vectors and Vector Functions | |
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| Vectors | |
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| The Dot Product | |
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| Vector Functions | |
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| Review | |
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| Limits and Rates of Change | |
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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 Law | |
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| The Precise Definition of a Limit | |
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| Continuity | |
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| Limits at Infinity | |
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| Horizontal Asymptotes | |
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| Tangents, Velocities, and Other Rates of Change | |
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| Review | |
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| Derivatives | |
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| Derivatives | |
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| Differentiation Formulas | |
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| Rates of Change in the Natural and Social Sciences | |
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| Derivatives of Trigonometric Functions | |
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| The Chain Rule | |
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| Implicit Differentiation | |
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| Derivatives of Vector Functions | |
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| Higher Derivatives | |
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| Slopes and Tangents of Parametric Curves | |
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| Related Rates | |
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| Differentials; Linear and Quadratic Approximations | |
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| Newton's Method | |
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| Review | |
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| Problems Plus | |
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| Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions | |
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| Exponential Functions and Their Derivatives | |
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| Inverse Functions | |
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| Logarithmic Functions | |
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| Derivatives of Logarithmic Functions | |
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| Exponential Growth and Decay | |
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| Inverse Trigonometric Functions | |
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| Hyperbolic Functions | |
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| Indeterminate Forms and L'Hospital's Rule | |
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| Review | |
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| Applications Plus | |
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| Applications of Differentiation | |
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| What does f Say about f? | |
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| Maximum and Minimum Values | |
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| Derivatives and the Shapes of Curves | |
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| Graphing with Calculus and Calculators | |
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| Applied Maximum and Minimum Problems | |
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| Applications to Economics | |
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| Antiderivatives | |
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| Review | |
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| Problems Plus | |
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| Integrals | |
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| Sigma Notation | |
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| Area | |
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| The Definite Integral | |
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| The Fundamental Theorem of Calculus | |
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| The Substitution Rule | |
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| The Logarithm Defined as an Integral | |
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| Review | |
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| Applications Plus | |
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| Applications of Integration | |
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| Areas between Curves | |
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| Volume | |
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| Volumes by Cylindrical Shells | |
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| Work | |
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| Average Value of a Function | |
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| Review | |
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| Problems Plus | |
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| Techniques of Integration | |
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| Integration by Parts | |
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| Trigonometric Integrals | |
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| Trigonometric Substitution | |
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| Integration of Rational Functions by Partial Fractions | |
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| Rationalizing Substitutions | |
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| Strategy for Integration | |
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| Using Tables of Integrals and Computer Algebra Systems | |
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| Approximate Integration | |
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| Improper Integrals | |
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| Review | |
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| Applications Plus | |
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| Further Applications of Integration | |
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| Differential Equations | |
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| First-Order Linear Equations | |
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| Arc Length | |
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| Area of Surface of Revolution | |
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| Moments and Centers of Mass | |
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| Hydrostatic Pressure and Force | |
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| Applications to Economics and Biology | |
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| Review | |
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| Problems Plus | |
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| Infinite Sequences and Series | |
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| Sequences | |
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| Series | |
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| The Integral Test and Comparison Tests | |
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| Other Convergence Tests | |
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| Power Series | |
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| Representation of Functions as Power Series | |
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| Taylor and Maclaurin Series | |
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| The Binomial Series | |
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| Writing Project: How Newton Discovered the Binomial Series | |
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| Applications of Taylor Polynomials | |
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| Review | |
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| Applications Plus | |
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| Three-Dimensional Analytic Geometry and Vectors | |
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| Three-Dimensional Coordinate Systems | |
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| Vectors and the Dot Product in Three Dimension | |
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| The Cross Product | |
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| Equations of Lines and Planes | |
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| Quadric Surfaces | |
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| Vector Functions and Space Curves | |
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| Arc Length and Curvature | |
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| Motion in Space | |
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| Review | |
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| Applications Plus | |
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| Partial Derivatives | |
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| Functions of Several Variables | |
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| Limits and Continuity | |
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| Partial Derivatives | |
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| Tangent Planes and Differentials | |
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| The Chain Rule | |
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| Directional Derivatives and the Gradient Vector | |
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| Maximum and Minimum Values | |
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| Lagrange Multipliers | |
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| Review | |
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| Problems Plus | |
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| Multiple Integrals | |
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| Double Integrals over Rectangles | |
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| Iterated Integrals | |
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| Double Integrals over General Regions | |
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| Polar Coordinates | |
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| Applications of Double Integrals | |
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| Surface Area | |
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| Triple Integrals | |
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| Cylindrical and Spherical Coordinates | |
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| Triple Integrals in Cylindrical and Spherical Coordinates | |
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| Change of Variables in Multiple Integrals | |
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| Review | |
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| Applications Plus | |
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| Vector Calculus | |
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| Vector Fields | |
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| Line Integrals | |
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| The Fundamental Theorem for Line Integrals | |
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| Green's Theorem | |
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| Curl and Divergence | |
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| Parametric Surfaces and their Areas | |
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| Surface Integrals | |
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| Stoke's Theorem | |
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| The Divergence Theorem | |
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| Summary | |
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| Review | |
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| Problems Plus | |
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| Second-Order Differential Equations | |
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| Second-Order Linear Equations | |
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| Nonhomogeneous Linear Equations | |
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| Applications of Second-Order Differential Equations | |
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| Using Series to Solve Differential Equations | |
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| Review | |
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| Problems Plus | |
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| Numbers, Inequalities, and Absolute Values | |
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| Coordinate Geometry and Lines | |
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| Graphs of Second-Degree Equations | |
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| Trigonometry | |
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| Mathematical Induction | |
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| Proofs of Theorems | |
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| Lies My Calculator and Computer Told Me | |
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| Complex Numbers | |
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| Conic Sections | |
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| Conic Sections in Polar Coordinates | |
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| Answers to Odd-Numbered Exercises | |
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| Index | |