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| Before Calculus | |
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| Functions | |
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| New Functions from Old | |
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| Families of Functions | |
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| Inverse Functions; Inverse Trigonometric Functions | |
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| Exponential and Logarithmic Functions | |
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| Limits and Continuity | |
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| Limits (An Intuitive Approach) | |
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| Computing Limits | |
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| Limits at Infinity; End Behavior of a Function | |
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| Limits (Discussed More Rigorously) | |
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| Continuity | |
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| Continuity of Trigonometric, Exponential, and Inverse Functions | |
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| The Derivative | |
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| Tangent Lines and Rates of Change | |
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| The Derivative Function | |
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| Introduction to Techniques of Differentiation | |
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| The Product and Quotient Rules | |
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| Derivatives of Trigonometric Functions | |
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| The Chain Rule | |
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| Topics in Differentiation | |
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| Implicit Differentiation | |
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| Derivatives of Logarithmic Functions | |
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| Derivatives of Exponential and Inverse Trigonometric Functions | |
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| Related Rates | |
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| Local Linear Approximation; Differentials | |
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| L'H�pital's Rule; Indeterminate Forms | |
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| The Derivative in Graphing and Applications | |
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| Analysis of Functions I: Increase, Decrease, and Concavity | |
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| Analysis of Functions II: Relative Extrema; Graphing Polynomials | |
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| Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents | |
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| Absolute Maxima and Minima | |
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| Applied Maximum and Minimum Problems | |
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| Rectilinear Motion | |
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| Newton's Method | |
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| Rolle's Theorem; Mean-Value Theorem | |
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| Integration | |
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| An Overview of the Area Problem | |
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| The Indefinite Integral | |
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| Integration by Substitution | |
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| The Definition of Area as a Limit; Sigma Notation | |
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| The Definite Integral | |
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| The Fundamental Theorem of Calculus | |
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| Rectilinear Motion Revisited Using Integration | |
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| Average Value of a Function and its Applications | |
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| Evaluating Definite Integrals by Substitution | |
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| Logarithmic and Other Functions Defined by Integrals | |
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| Applications of the Definite Integral in Geometry, Science, and Engineering | |
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| Area Between Two Curves | |
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| Volumes by Slicing; Disks and Washers | |
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| Volumes by Cylindrical Shells | |
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| Length of a Plane Curve | |
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| Area of a Surface of Revolution | |
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| Work | |
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| Moments, Centers of Gravity, and Centroids | |
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| Fluid Pressure and Force | |
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| Hyperbolic Functions and Hanging Cables | |
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| Principles of Integral Evaluation | |
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| An Overview of Integration Methods | |
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| Integration by Parts | |
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| Integrating Trigonometric Functions | |
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| Trigonometric Substitutions | |
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| Integrating Rational Functions by Partial Fractions | |
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| Using Computer Algebra Systems and Tables of Integrals | |
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| Numerical Integration; Simpson's Rule | |
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| Improper Integrals | |
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| Mathematical Modeling with Differential Equations | |
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| Modeling with Differential Equations | |
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| Separation of Variables | |
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| Slope Fields; Euler's Method | |
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| First-Order Differential Equations and Applications | |
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| Infinite Series | |
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| Sequences | |
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| Monotone Sequences | |
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| Infinite Series | |
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| Convergence Tests | |
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| The Comparison, Ratio, and Root Tests | |
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| Alternating Series; Absolute and Conditional Convergence | |
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| Maclaurin and Taylor Polynomials | |
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| Maclaurin and Taylor Series; Power Series | |
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| Convergence of Taylor Series | |
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| Differentiating and Integrating Power Series; Modeling with Taylor Series | |
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| Parametric and Polar Curves; Conic Sections | |
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| Parametric Equations; Tangent Lines and Arc Length for Parametric Curves | |
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| Polar Coordinates | |
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| Tangent Lines, Arc Length, and Area for Polar Curves | |
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| Conic Sections | |
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| Rotation of Axes; Second-Degree Equations | |
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| Conic Sections in Polar Coordinates | |