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| Precalculus Review | |
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| Real Numbers, Functions, and Graphs | |
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| Linear and Quadratic Functions | |
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| The Basic Classes of Functions | |
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| Trigonometric Functions | |
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| Inverse Functions | |
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| Exponential and Logarithmic Functions | |
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| Technology Calculators and Computers | |
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| Limits | |
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| Limits, Rates of Change, and Tangent Lines | |
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| Limits: A Numerical and Graphical Approach2.3 Basic Limit Laws | |
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| Limits and Continuity | |
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| Evaluating Limits Algebraically | |
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| Trigonometric Limits | |
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| Limits at Infinity | |
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| Intermediate Value Theorem | |
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| The Formal Definition of a Limit | |
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| Differentiation | |
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| Definition of the Derivative | |
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| The Derivative as a Function | |
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| Product and Quotient Rules | |
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| Rates of Change | |
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| Higher Derivatives | |
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| Trigonometric Functions | |
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| The Chain Rule | |
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| Derivatives of Inverse Functions | |
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| Derivatives of General Exponential and Logarithmic Functions | |
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| Implicit Differentiation | |
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| Related Rates | |
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| Applications of the Derivative | |
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| Linear Approximation and Applications | |
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| Extreme Values | |
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| The Mean Value Theorem and Monotonicity | |
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| The Shape of a Graph | |
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| L'Hopital's Rule | |
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| Graph Sketching and Asymptotes | |
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| Applied Optimization | |
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| Newton's Method | |
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| Antiderivatives | |
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| The Integral | |
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| Approximating and Computing Area | |
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| The Definite Integral | |
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| The Fundamental Theorem of Calculus, Part I | |
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| The Fundamental Theorem of Calculus, Part II | |
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| Net Change as the Integral of a Rate | |
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| Substitution Method | |
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| Further Transcendental Functions | |
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| Exponential Growth and Decay | |
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| Applications of the Integral | |
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| Area Between Two Curves | |
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| Setting Up Integrals: Volume, Density, Average Value | |
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| Volumes of Revolution | |
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| The Method of Cylindrical Shells | |
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| Work and Energy | |
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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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| Integrals Involving Hyperbolic and Inverse Hyperbolic Functions | |
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| The Method of Partial Fractions | |
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| Improper Integrals | |
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| Probability and Integration | |
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| Numerical Integration | |
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| Further Applications of the Integral and Taylor Polynomials | |
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| Arc Length and Surface Area | |
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| Fluid Pressure and Force | |
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| Center of Mass | |
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| Taylor Polynomials | |
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| Introduction to Differential Equations | |
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| Solving Differential Equations | |
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| Models Involving y' = k (y-b) | |
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| Graphical and Numerical Methods | |
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| The Logistic Equation | |
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| First-Order Linear Equations | |
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| Infinite Series | |
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| Sequences | |
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| Summing an Infinite Series | |
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| Convergence of Series with Positive Terms | |
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| Absolute and Conditional Convergence | |
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| The Ratio and Root Tests | |
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| Power Series | |
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| Taylor Series | |
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| Parametric Equations, Polar Coordinates, and Conic Sections | |
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| Parametric Equations | |
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| Arc Length and Speed | |
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| Polar Coordinates | |
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| Area and Arc Length in Polar Coordinates | |
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| Conic Sections | |
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| Vector Geometry | |
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| Vectors in the Plane | |
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| Vectors in Three Dimensions | |
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| Dot Product and the Angle Between Two Vectors | |
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| The Cross Product | |
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| Planes in Three-Space | |
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| A Survey of Quadric Surfaces | |
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| Cylindrical and Spherical Coordinates | |
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| Calculus of Vector-Valued Functions | |
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| Vector-Valued Functions | |
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| Calculus of Vector-Valued Functions | |
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| Arc Length and Speed | |
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| Curvature | |
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| Motion in Three-Space | |
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| Planetary Motion According to Kepler and Newton | |
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| Differentiation in Several Variables | |
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| Functions of Two or More Variables | |
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| Limits and Continuity in Several Variables | |
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| Partial Derivatives | |
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| Differentiability and Tangent Planes | |
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| The Gradient and Directional Derivatives | |
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| The Chain Rule | |
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| Optimization in Several Variables | |
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| Lagrange Multipliers: Optimizing with a Constraint | |
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| Multiple Integration | |
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| Integration in Variables | |
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| Double Integrals over More General Regions | |
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| Triple Integrals | |
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| Integration in Polar, Cylindrical, and Spherical Coordinates | |
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| Applications of Multiplying Integrals | |
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| Change of Variables | |
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| Line and Surface Integrals | |
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| Vector Fields | |
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| Line Integrals | |
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| Conservative Vector Fields | |
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| Parametrized Surfaces and Surface Integrals | |
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| Surface Integrals of Vector Fields | |
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| Fundamental Theorems of Vector Analysis | |
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| Green's Theorem | |
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| Stokes' Theorem | |
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| Divergence Theorem | |
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| Appendices | |
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| The Language of Mathematics | |
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| Properties of Real Numbers | |
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| Mathematical Induction and the Binomial Theorem | |
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| Additional Proofs of Theorems | |
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| Taylor Polynomials | |
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| Answers to Odd-Numbered Exercises | |
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| References | |
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| Photo Credits | |
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| Index | |