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 BC |
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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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Polynomial and Rational Functions |
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Vectors and Vector-Valued Functions |
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Polar Coordinates and Graphs |
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Parametric Equations and Conic... |
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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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Parametric Derivatives |
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Differentiation with Polar Curves |
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Differentiation of Vector-Valued |
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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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L'Hospital's Rule |
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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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Integration by Parts |
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Integration by Partial Fractions |
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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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Improper Integrals |
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Net Change and Displacement |
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Volume |
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Separable Differential Equations |
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Numerical Solutions to Differential... |
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Logistic Growth |
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Work |
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Arc Length and Surface of Revolution |
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Integration of Vector-Valued... |
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Parametric Integrals |
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Polar Integrals |
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Other Applications of Definite... |
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Sequences |
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Series |
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Estimating Sums |
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Other Tests for Convergence |
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Power Series |
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Taylor and Maclaurin series |
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