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| Precalculus Review | |
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| What is Calculus? | |
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| Review of Elementary Mathematics | |
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| Review of Inequalities | |
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| Coordinate Plane | |
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| Analytic Geometry | |
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| Functions | |
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| The Elementary Functions | |
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| Combinations of Functions | |
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| A Note on Mathematical Proof; Mathematical Induction | |
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| Limits and Continuity | |
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| The Limit Process (An Intuitive Introduction) | |
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| Definition of Limit | |
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| Some Limit Theorems | |
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| Continuity | |
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| The Pinching Theorem; Trigonometric Limits | |
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| Two Basic Theorems | |
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| The Derivative; The Process of Differentiation | |
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| The Derivative | |
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| Some Differentiation Formulas | |
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| Thed/dx Notation Derivatives of Higher Order | |
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| The Derivative as a Rate of Change | |
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| The Chain Rule | |
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| Differentiating the Trigonometric Functions | |
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| Implicit Differentiation Rational Powers | |
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| The Mean-Value Theorem; Applications of the First and Second Derivatives | |
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| The Mean-Value Theorem | |
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| Increasing and Decreasing Functions | |
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| Local Extreme Values | |
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| Endpoint Extreme Values; Absolute Extreme Values | |
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| Some Max-Min Problems | |
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| Concavity and Points of Inflection | |
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| Vertical and Horizontal Asymptotes; Vertical Tangents and Cusps | |
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| Some Curve Sketching | |
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| Velocity and Acceleration; Speed | |
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| Related Rates of Change Per Unit Time | |
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| Differentials | |
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| Newton-Raphson Approximations | |
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| Integration | |
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| An Area Problem; A Speed-Distance Problem | |
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| The Definite Integral of a Continuous Function | |
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| The Function f(x) = Integral from a to x of f(t) dt | |
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| The Fundamental Theorem of Integral Calculus | |
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| Some Area Problems | |
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| Indefinite Integrals | |
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| Working Back from the Chain Rule; theu-Substitution | |
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| Additional Properties of the Definite Integral | |
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| Mean-Value Theorems for Integrals; Average Value of a Function | |
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| Some Applications of the Integral | |
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| More on Area | |
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| Volume by Parallel Cross-Sections; Discs and Washers | |
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| Volume by the Shell Method | |
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| The Centroid of a Region; PappusA?s Theorem on Volumes | |
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| The Notion of Work | |
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| Fluid Force | |
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| The Transcendental Functions | |
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| One-to-One Functions; Inverse Functions | |
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| The Logarithm Function, Part I | |
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| The Logarithm Function, Part II | |
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| The Exponential Function | |
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| Arbitrary Powers; Other Bases | |
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| Exponential Growth and Decay | |
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| The Inverse Trigonometric Functions | |
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| The Hyperbolic Sine and Cosine | |
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| The Other Hyperbolic Functions | |
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| Techniques of Integration | |
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| Integral Tables and Review | |
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| Integration by Parts | |
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| Powers and Products of Trigonometric Functions | |
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| Integrals Featuring Square Root of (a^2 - x^2), Square Root of (a^2 + x^2), and Square Root of (x^2 - a^2) | |
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| Rational Functions; Partial Functions | |
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| Some Rationalizing Substitutions | |
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| Numerical Integration | |
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| Differential Equations | |
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| First-Order Linear Equations | |
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| Integral Curves; Separable Equations | |
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| The Equationya??a?? +aya??+by = 0 | |
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| The Conic Sections; Polar Coordinates; Parametric Equations | |
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| Geometry of Parabola, Ellipse, Hyperbola | |
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| Polar Coordinates | |
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| Graphing in Polar Coordinates | |
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| Area in Polar Coordinates | |
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| Curves G | |