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| Basics | |
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| Preview | |
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| Number Systems | |
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| Planar Coordinates and Graphing in the Plane | |
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| Lines and Their Slopes | |
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| Functions and Their Graphs | |
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| Combining Functions | |
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| Trigonometry | |
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| Summary of Key Topics | |
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| Review Exercises for Chapter 1 | |
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| Genesis and Development | |
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| Limits | |
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| Preview | |
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| The Concept of Limit | |
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| Limit Theorems | |
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| Continuity | |
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| Infinite Limits and Asymptotes | |
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| Limits of Sequences | |
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| Exponential and Logarithmic Functions | |
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| Summary of Key Topics | |
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| Review Exercises | |
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| Genesis and Development | |
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| The Derivative | |
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| Preview | |
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| Rates of Change and Tangent Lines | |
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| The Derivative | |
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| Rules for Differentiation | |
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| Differentiation of Some Basic Functions | |
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| The Chain Rule | |
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| Derivatives of Inverse Functions | |
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| Higher Derivatives | |
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| Implicit Differentiation | |
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| Differentials and Approximation of Functions | |
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| Other Transcendental Functions | |
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| Summary of Key Topics | |
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| Review Exercises | |
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| Genesis and Development | |
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| Applications of the Derivative | |
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| Preview | |
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| Related Rates | |
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| The Mean Value Theorem | |
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| Maxima and Minima of Functions | |
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| Applied Maximum-Minimum Problems | |
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| Concavity | |
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| Graphing Functions | |
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| L'Hopital's Rule | |
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| The Newton-Raphson Method | |
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| Antidifferentiation and Applications | |
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| Summary of Key Topics | |
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| Review Exercises | |
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| Genesis and Development | |
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| The Integral | |
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| Preview | |
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| Introduction to Integration-The Area Problem | |
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| The Riemann Integral | |
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| Properties of the Integral | |
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| The Fundamental Theorem of Calculus | |
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| A Calculus Approach to the Logarithm and Exponential Functions | |
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| Integration by Substitution | |
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| More on the Calculation of Area | |
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| Numerical Techniques of Integration | |
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| Summary of Key Topics | |
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| Review Exercises | |
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| Genesis and Development | |
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| Techniques of Integration | |
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| Preview | |
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| Integration by Parts | |
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| Powers and Products of Trigonometric Functions | |
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| Trigonometric Substitution | |
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| Partial Fractions-Linear Factors | |
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| Partial Fractions-Irreducible Quadratic Factors | |
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| Improper Integrals-Unbounded Integrands | |
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| Improper Integrals-Unbounded Intervals | |
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| Summary of Key Topics | |
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| Review Exercises | |
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| Genesis and Development | |
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| Applications of the Integral | |
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| Preview | |
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| Volumes | |
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| Arc Length and Surface Area | |
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| The Average Value of a Function | |
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| Center of Mass | |
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| Work | |
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| First Order Differential Equations-Separable Equations | |
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| First Order Differential Equations-Linear Equations | |
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| Summary of Key Topics | |
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| Review Exercises | |
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| Genesis and Development | |
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| Infinite Series | |
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| Preview | |
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| Series | |
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| The Divergence Test and The Integral Test | |
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| The Comparison Tests | |
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| Alternating Series | |
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| The Ratio and Root Tests | |
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| Introduction to Power Series | |
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| Representing Functions by Power Series | |
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| Taylor Series | |
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| Summary of Key Topics | |
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| Review Exercises | |
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| Genesis and Development | |
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| Vectors | |
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| Preview | |
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| Vectors in the Plane | |
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| Vectors in Three-Dimensional Space | |
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| The Dot Product and Applications | |
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| The Cross Product and Triple Product | |
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| Lines and Planes in Space | |
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| Summary of Key Topics in Chapter 9 | |
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| Review Exercises for Chapter 9 | |
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| Genesis and Development | |
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| Curves in Space | |
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| Preview | |
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| Vector-Valued Functions-Limits, Derivatives, and Continuity | |
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| Velocity and Acceleration | |
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| Tangent Vectors and Arc Length | |
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| Curvature | |
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| Applications of Vector-Valued Functions to Motion | |
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| Summary of Key Topics in Chapter 10 | |
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| Review Exercises for Chapter 10 | |
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| Genesis and Development | |
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| Functions of Several Variables | |
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| Preview | |
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| Functions of Several Variables | |
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| Cylinders and Quadric Surfaces | |
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| Limits and Continuity | |
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| Partial Derivatives | |
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| Differentiability and The Chain Rule | |
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| Gradients and Directional Derivatives | |
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| Tangent Planes | |
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| Maximum-Minimum Problems | |
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| Lagrange Multipliers | |
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| Summary of Key Topics in Chapter 11 | |
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| Review Exercises for Chapter 11 | |
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| Genesis and Development | |
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| Multiple Integrals | |
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| Preview | |
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| Double Integrals over Rectangular Regions | |
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| Integration over More General Regions | |
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| Calculation of Volumes of Solids | |
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| Polar Coordinates | |
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| Integrating in Polar Coordinates | |
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| Triple Integrals | |
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| Physical Applications | |
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| Other Coordinate Systems | |
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| Summary of Key Topics in Chapter 12 | |
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| Review Exercises for Chapter 12 | |
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| Genesis and Development | |
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| Vector Calculus | |
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| Preview | |
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| Vector Fields | |
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| Line Integrals | |
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| Conservative Vector Fields and Path Independence | |
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| Divergence, Gradient, and Curl | |
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| Green's Theorem | |
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| Surface Integrals | |
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| Stokes's Theorem | |
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| The Divergence Theorem | |
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| Summary of Key Topics in Chapter 13 | |
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| Review Exercises for Chapter 13 | |
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| Genesis and Development | |