This is an outline of topics covered. Additional Topics can be requested by a student. Programs will be customized for the individual student.
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| Prerequisites |
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Before studying calculus, all students should complete four years of secondaryMathematics designed for college-bound students: courses in which they studyAlgebra, geometry, trigonometry, analytic geometry, and elementary functions.These Functions include linear, polynomial, rational, exponential,logarithmic,Trigonometric, Inverse trigonometric and piecewise-defined functions. In particular, Before studying calculus, Students must be familiar with the properties of functions, The algebra of Functions and the graphs of functions. Students must also understand the languageOf functions (domain and range, odd and even, periodic, symmetry,Zeros, intercepts And so on) and know the values of the trigonometric functions at the numbers , and their multiples. |
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| Calculus AB |
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| This is an outline of topics covered. Additional Topics can be requested by a student. Programs will be customized for the individual student. |
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Functions and Function Notation |
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Absolute Value and Piecewise Defined... |
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Inequalities |
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Composition and Combination of... |
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Exponential and Logarithmic Functions |
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Transformation of Functions |
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Trigonometric Functions |
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Power, Polynomial and Rational... |
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Intuitive Definition of a Limit |
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Algebraic Techniques for Finding... |
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One-Sided Limits |
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Infinite Limits |
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Limits at Infinity |
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Limits of Special Trigonometric... |
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Continuity |
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Definition of the Derivative |
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Differentiation Rules |
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The Chain Rule |
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Derivatives of Exponential Functions |
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Derivative of Logarithmic Functions |
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Derivatives of Inverse Functions |
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Differentiability and Continuity |
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Implicit Differentiation |
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Logarithmic Differentiation |
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Tangent and Normal Lines |
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Position, Velocity, and Acceleration... |
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Related Rates |
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Relative Extrema and the First... |
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Concavity and the Second Derivative... |
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Absolute Extrema and Optimization |
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Rolle's Rule and the Mean Value... |
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Differentials |
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Differential Equations and Slope... |
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Antiderivatives |
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The Chain Rule for Antiderivatives |
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Antiderivatives of Exponentials |
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Antiderivatives and Logarithms |
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Antiderivatives and Inverse... |
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Trigonometric Substitutions |
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The Definite Integral |
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Fundamental Theorem of Calculus |
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Net Change and Displacement |
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Volume |
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Separable Differential Equations |
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Work |
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Other Applications of Definite... |
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