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| Preliminaries | |
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| Lines | |
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| Functions and Their Graphs | |
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| The Trigonometric Functions | |
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| Combining Functions | |
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| Graphing Calculators and Computers | |
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| Mathematical Models | |
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| Chapter Review | |
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| Limits | |
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| An Intuitive Introduction to Limits | |
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| Techniques for Finding Limits | |
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| A Precise Definition of a Limit | |
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| Continuous Functions | |
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| Tangent Lines and Rates of Change | |
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| Chapter Review | |
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| Problem-Solving Techniques | |
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| Challenge Problems | |
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| The Derivative | |
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| The Derivative | |
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| Basic Rules of Differentiation | |
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| The Product and Quotient Rules | |
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| The Role of the Derivative in the Real World | |
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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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| Related Rates | |
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| Differentials and Linear Approximations | |
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| Chapter Review | |
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| Problem-Solving Techniques | |
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| Challenge Problems | |
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| Applications Of The Derivative | |
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| Extrema of Functions | |
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| The Mean Value Theorem | |
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| Increasing and Decreasing Functions and the FirSt. Derivative TeSt. Concavity and Inflection Points | |
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| Limits Involving Infinity | |
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| Asymptotes | |
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| Curve Sketching | |
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| Optimization Problems | |
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| Newton's Method | |
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| Chapter Review | |
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| Problem-Solving Techniques | |
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| Challenge Problems | |
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| Integration | |
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| Indefinite Integrals | |
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| Integration by Substitution | |
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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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| Numerical Integration | |
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| Chapter Review | |
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| Problem-Solving Techniques | |
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| Challenge Problems | |
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| Applications Of The Definite Integral | |
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| Areas Between Curves | |
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| Volumes: Disks, Washers, and Cross Sections | |
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| Volumes Using Cylindrical Shells | |
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| Arc Length and Areas of Surfaces of Revolution | |
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| Work | |
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| Fluid Pressure and Force | |
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| Moments and Centers of Mass | |
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| Chapter Review | |
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| Problem-Solving Techniques | |
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| Challenge Problems | |
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| The Transcendental Functions | |
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| The Natural Logarithmic Function | |
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| Inverse Functions | |
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| Exponential Functions | |
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| General Exponential and Logarithmic Functions | |
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| Inverse Trigonometric Functions | |
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| Hyperbolic Functions | |
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| Indeterminate Forms and L'H?pital's Rule | |
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| Chapter Review | |
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| Challenge Problems | |
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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 Substitutions | |
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| The Method of Partial Fractions | |
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| Integration Using Tables of Integrals and CAS | |
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| Improper Integrals | |
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| Chapter Review | |
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| Problem-Solving Techniques | |
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| Challenge Problems | |
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| Differential Equations | |
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| Differential Equations: Separable Equations | |
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| Direction Fields and Euler's Method | |
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| The Logistic Equation | |
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| First-Order Linear Differential Equations | |
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| Chapter Review | |
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| Challenge Problems | |
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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. The Comparison Tests | |
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| Alternating Series | |
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| Absolute Convergence | |
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| The Ratio and Root Tests | |
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| Power Series | |
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| Taylor and Maclaurin Series | |
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| Approximation by Taylor Polynomials | |
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| Chapter Review | |
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| Problem-Solving Techniques | |
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| Challenge Problems | |
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| Conic Sections, Parametric Equations, And Polar Coordinates | |
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| Conic Sections | |
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| Plane Curves and Parametric Equations | |
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| The Calculus of Parametric Equations | |
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| Polar Coordinates | |
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| Areas and Arc Lengths in Polar Coordinates | |
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| Conic Sections in Polar Coordinates | |
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| Chapter Review | |
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| Challenge Problems | |
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| Vectors And The Geometry Of Space | |
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| Vectors in the Plane | |
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| Coordinate Systems and Vectors in Three-Space | |
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| The Dot Product | |
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| The Cross Product | |
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| Lines and Planes in Space | |
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| Surfaces in Space | |
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| Cylindrical and Spherical Coordinates | |
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| Chapter Review | |
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| Challenge Problems | |
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| Vector-Valued Functions | |
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| Vector-Valued Functions and Space Curves | |
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| Differentiation and Integration of Vector- Valued | |
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| Functions | |
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| Arc Length and Curvature | |
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| Velocity and Acceleration | |
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| Tangential and Normal Components of Acceleration | |
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| Chapter Review | |
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| Challenge Problems | |
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| Functions Of Several Variables | |
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| Functions of Two or More Variables | |
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| Limits and Continuity | |
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| Partial Derivatives | |
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| Differentials | |
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| The Chain Rule | |
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| Directional Derivatives and Gradient Vectors | |
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| Tangent Planes and Normal Lines | |
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| Extrema of Functions of Two Variables | |
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| Lagrange Multipliers | |
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| Chapter Review | |
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| Challenge Problems | |
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| Multiple Integrals Double Integrals | |
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| Iterated Integrals | |
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| Double Integrals in 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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| Triple Integrals in Cylindrical and Spherical Coordinates | |
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| Change of Variables in Multiple Integrals | |
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| Chapter Review | |
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| Challenge Problems | |
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| Vector Analysis | |
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| Vector Fields | |
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| Divergence and Curl | |
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| Line Integrals | |
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| Independence of Path and Conservative Vector Fields | |
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| Green's Theorem | |
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| Parametric Surfaces | |
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| Surface Integrals | |
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| The Divergence Theorem | |
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| Stoke's Theorem | |
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| Chapter Review | |
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| Challenge Problems | |
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| Appendices | |
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| The Real Number Line, Inequalities, and Absolute Value | |
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| Proofs of Selected Theorems | |