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Precalculus Review | |
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Algebra | |
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Functions | |
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Trigonometry | |
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Limits of Functions | |
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Introduction to Limits | |
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Definition of Limits | |
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Techniques for Finding Limits | |
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Limits Involving Infinity | |
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Continuous Functions | |
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Review Exercises | |
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The Derivative | |
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Tangent Lines and Rates of Change | |
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Definition of Derivative | |
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Techniques of Differentiation | |
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Derivatives of the Trigonometric Functions | |
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Increments and Differentials | |
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The Chain Rule | |
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Implicit Differentiation | |
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Related Rates | |
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Review Exercises | |
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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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The First Derivative Test | |
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Concavity and the Second Derivative Test | |
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Summary of Graphical Methods | |
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Optimization Problems | |
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Rectlinear Motion and Other Applications | |
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Newton's Method | |
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Review Exercises | |
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Integrals | |
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Antiderivatives and Indefinite Integrals | |
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Change of Variables in Indefinite Integrals | |
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Summation Notation and Area | |
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The Definite Integral | |
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Properties of the Definite Integral | |
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The Fundamental Theorem of Calculus | |
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Numerical Integration | |
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Review Exercises | |
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Applications of the Definite Integral | |
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Area | |
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Solids of Revolution | |
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Volumes by Cylindrical Shells | |
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Volumes by Cross Sections | |
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Arc Length and Surfaces of Revolution | |
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Work | |
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Moments and Centers of Mass | |
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Other Applications | |
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Review Exercises | |
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Logarithmic and Exponential Functions | |
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Inverse Functions | |
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The Natural Logarithmic Function | |
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The Natural Exponential Function | |
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Integration | |
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General Exponential and Logarithmic Functions | |
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Laws of Growth and Decay | |
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Review Exercises | |
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Inverse Trigonometric and Hyperbolic Functions | |
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Inverse Trigonometric Functions | |
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Derivative and Integrals | |
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Hyperbolic Functions | |
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Inverse Hyperbolic Functions | |
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Review Exercises | |
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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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Integrals of Rational Functions | |
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Integrals Involving Quadratic Expressions | |
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Miscellaneous Substitutions | |
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Tables of Integrals | |
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Review Exercises | |
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Indeterminate Forms and Improper Integrals | |
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The Indeterminate Forms 0/0 and ?/? | |
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Other Indeterminate Forms | |
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Integrals with Infinite Limits of Integration | |
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Integrals with Discontinuous Integrands | |
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Review Exercises | |
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Infinite Series | |
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Sequences | |
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Convergent of Divergent Series | |
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Positive-Term Series | |
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The Rational and Root Tests | |
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Alternation Series and Absolute Convergence | |
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Power Series | |
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Power Series Representations of Functions | |
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Maclaurin and Taylor Series | |
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Applications of Taylor Polynomials | |
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The Binomial Series | |
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Review Exercises | |
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Topics From Analytic Geometry | |
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Parabolas | |
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Ellipses | |
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Hyperbolas | |
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Rotation of Axes | |
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Review Exercises | |
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Plane Curves and Polar Coordinates | |
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Plane Curves | |
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Tangent Lines and Arc Length | |
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Polar Coordinates | |
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Integrals in Polar Coordinates | |
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Polar Equations of Conics | |
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Review Exercises | |
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Vectors and Surfaces | |
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Vectors in Two Dimensions | |
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Vectors in Three Dimensions | |
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The Dot Product | |
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The Vector Product | |
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Lines and Planes | |
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Surfaces | |
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Review Exercises | |
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Vector-Valued Functions | |
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Vector-Valued Functions and Space Curves | |
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Limits, Derivatives, and Integrals | |
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Motion | |
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Curvature | |
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Tangential and Normal Components of Acceleration | |
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Kepler's Laws | |
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Review Exercises | |
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Partial Differentiation | |
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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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Increments and Differentials | |
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Chain Rules | |
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Directional Derivatives | |
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Tangent Planes and Normal Lines | |
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Extrema of Functions of Several Variables | |
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Lagrange Multipliers | |
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Review Exercises | |
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Multiple Integrals | |
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Double Integrals | |
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Area and Volume | |
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Double Integrals in Polar Coordinates | |
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Surface Area | |
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Triple Integrals | |
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Moments and Center of Mass | |
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Cylindrical Coordinates | |
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Spherical Coordinates | |
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Change of Variables and Jacobians | |
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Review Exercises | |
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Vector Calculus | |
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Vector Fields | |
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Line Integrals | |
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Independence of Path | |
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Green's Theorem | |
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Surface Integrals | |
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The Divergence Theorem | |
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Stoke's Theorem | |
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Review Exercises | |
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Differential Equations | |
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Seperable Differential Equations | |
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First-Order Linear Differential Equations | |
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Second-Order Linear Differential Equations | |
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Nonhomogeneous Linear Differential Equations | |
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Vibrations | |
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Series Solutions | |
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Review Exercises | |
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Mathematical Induction | |
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Theorems on Limits and Integrals | |
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Tables | |
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Table Of Integrals | |
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Answers To Odd-Numbered Exercises | |
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Index | |