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| Functions, Graphs, and Models | |
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| Functions and Mathematical Modeling | |
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| Graphs of Equations and Functions | |
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| Polynomials and Algebraic Functions | |
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| Transcendental Functions | |
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| Preview: What Is Calculus? | |
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| Prelude to Calculus | |
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| Tangent Lines and Slope Predictors | |
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| The Limit Concept | |
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| More about Limits | |
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| The Concept of Continuity | |
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| The Derivative | |
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| The Derivative and Rates of Change | |
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| Basic Differentiation Rules | |
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| The Chain Rule | |
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| Derivatives of Algebraic Functions | |
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| Maxima and Minima of Functions on Closed Intervals | |
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| Applied Optimization Problems | |
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| Derivatives of Trigonometric Functions | |
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| Successive Approximations and Newton's Method | |
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| Additional Applications of the Derivative | |
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| Implicit Functions and Related Rates | |
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| Increments, Differentials, and Linear Approximation | |
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| Increasing and Decreasing Functions and the Mean Value Theorem | |
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| The First Derivative Test and Applications | |
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| Simple Curve Sketching | |
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| Higher Derivatives and Concavity | |
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| Curve Sketching and Asymptotes | |
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| The Integral | |
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| Introduction | |
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| Antiderivatives and Initial Value Problems | |
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| Elementary Area Computations | |
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| Riemann Sums and the Integral | |
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| Evaluation of Integrals | |
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| The Fundamental Theorem of Calculus | |
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| Integration by Substitution | |
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| Areas of Plane Regions | |
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| Numerical Integration | |
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| Applications of the Integral | |
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| Riemann Sum Approximations | |
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| Volumes by the Method of Cross Sections | |
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| Volumes by the Method of Cylindrical Shells | |
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| Arc Length and Surface Area of Revolution | |
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| Force and Work | |
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| Centroids of Plane Regions and Curves | |
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| Calculus of Transcendental Functions | |
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| Exponential and Logarithmic Functions | |
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| Indeterminate Forms and L'Hop?tal's Rule | |
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| More Indeterminate Forms | |
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| The Logarithm as an Integral | |
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| Inverse Trigonometric Functions | |
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| Hyperbolic Functions | |
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| Techniques of Integration | |
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| Introduction | |
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| Integral Tables and Simple Substitutions | |
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| Integration by Parts | |
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| Trigonometric Integrals | |
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| Rational Functions and Partial Fractions | |
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| Trigonometric Substitutions | |
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| Integrals Involving Quadratic Polynomials | |
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| Improper Integrals | |
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| Differential Equations | |
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| Simple Equations and Models | |
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| Slope Fields and Euler's Method | |
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| Separable Equations and Applications | |
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| Linear Equations and Applications | |
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| Population Models | |
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| Linear Second-Order Equations | |
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| Mechanical Vibrations | |
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| Polar Coordinates and Parametric Curves | |
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| Analytic Geometry and the Conic Sections | |
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| Polar Coordinates | |
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| Area Computations in Polar Coordinates | |
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| Parametric Curves | |
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| Integral Computations with Parametric Curves | |
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| Conic Sections and Applications | |
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| Infinite Series | |
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| Introduction | |
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| Infinite Sequences | |
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| Infinite Series and Convergence | |
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| Taylor Series and Taylor Polynomials | |
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| The Integral Test | |
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| Comparison Tests for Positive-Term Series | |
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| Alternating Series and Absolute Convergence | |
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| Power Series | |
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| Power Series Computations | |
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| Series Solutions of Differential Equations | |
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| Vectors, Curves, and Surfaces in Space | |
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| Vectors in the Plane | |
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| Three-Dimensional Vectors | |
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| The Cross Product of Vectors | |
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| Lines and Planes in Space | |
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| Curves and Motions in Space | |
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| Curvature and Acceleration | |
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| Cylinders and Quadric Surfaces | |
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| Cylindrical and Spherical Coordinates | |
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| Partial Differentiation | |
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| Introduction | |
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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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| Multivariable Optimization Problems | |
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| Increments and Linear Approximation | |
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| The Multivariable Chain Rule | |
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| Directional Derivatives and the Gradient Vector | |
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| Lagrange Multipliers and Constrained Optimization | |
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| Critical Points of Functions of Two Variables | |
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| Multiple Integrals | |
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| Double Integrals | |
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| Double Integrals over More General Regions | |
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| Area and Volume by Double Integration | |