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Calculus Topics

Limits

–Finding limits from graphs

–Finding limits algebraically - direct substitution

–Finding limits algebraically - when direct substitution is not possible

–Infinite limits - vertical asymptotes

–Limits at infinity - horizontal asymptotes

–Intermediate value theorem

–Squeeze theorem

Derivatives

–Definition of derivative

–Slope and equation of tangent line

–Derivative of trigonometric functions

–Derivative of exponential functions

–Product rule

–Quotient rule

–Implicit differentiation

–Derivative of inverse trigonometric functions

–Derivative of logarithmic functions

–Higher order derivatives

Derivative Applications

–Position velocity acceleration

–Critical number & maximum and minimum values

–l'Hospital's rule

–Curve sketching

–Optimization

–Related rates

–Rolle’s theorem

–Mean value theorem

–Linear approximation

–Quadratic approximation

–Demand, revenue, cost & profit

–Marginal revenue, and maximizing revenue & average revenue

–Marginal cost, and minimizing cost & average cost

–Marginal profit, and maximizing profit & average profit

–Elasticity of demand

Integrals

–Antiderivatives

–Definite integral

–Fundamental theorem of calculus

Integration Techniques

–U-Substitution

–Integration by parts

–Integration using trigonometric identities

–Trigonometric substitution

–Integration of rational functions by partial fractions

–Improper integrals

Integration Applications

–Areas between curves

–Volumes of solids with known cross-sections

–Volumes of solids of revolution - Disc method

–Volumes of solids of revolution - Shell method

–Average value of a function

–Consumer and producer surplus

–Continuous money flow

Differential Equations

–Introduction to differential equations

–Separable equations

–Applications to differential equations

Sequence and Series

–Introduction to sequences

–Monotonic and bounded sequences

–Introduction to infinite series

–Convergence and divergence of normal infinite series

–Convergence & divergence of geometric series

–Convergence & divergence of telescoping series

–Divergence of harmonic series

–Alternating series test

–Divergence test

–Comparison & limit comparison test

–Integral test

–Absolute & conditional convergence

–Radius and interval of convergence with power series

–Functions expressed as power series

–Taylor and maclaurin series

–Approximating functions with Taylor polynomials and error bounds

Parametric Equations and Polar Coordinates

–Defining curves with parametric equations

–Tangent and concavity of parametric equations

–Area of parametric equations

–Arc length and surface area of parametric equations

–Polar coordinates

–Tangents of polar curves

–Area of polar curves

–Arc length of polar curves

Derivative Applications

–Position velocity acceleration

–Critical number & maximum and minimum values

–l'Hospital's rule

–Curve sketching

–Optimization

–Related rates

–Rolle’s theorem

–Mean value theorem

–Linear approximation

–Quadratic approximation

–Demand, revenue, cost & profit

–Marginal revenue, and maximizing revenue & average revenue

–Marginal cost, and minimizing cost & average cost

–Marginal profit, and maximizing profit & average profit

–Elasticity of demand

Integrals

–Antiderivatives

–Definite integral

–Fundamental theorem of calculus

Integration Techniques

–U-Substitution

–Integration by parts

–Integration using trigonometric identities

–Trigonometric substitution

–Integration of rational functions by partial fractions

–Improper integrals

Integration Applications

–Areas between curves

–Volumes of solids with known cross-sections

–Volumes of solids of revolution - Disc method

–Volumes of solids of revolution - Shell method

–Average value of a function

–Consumer and producer surplus

–Continuous money flow

Differential Equations

–Introduction to differential equations

–Separable equations

–Applications to differential equations

Sequence and Series

–Introduction to sequences

–Monotonic and bounded sequences

–Introduction to infinite series

–Convergence and divergence of normal infinite series

–Convergence & divergence of geometric series

–Convergence & divergence of telescoping series

–Divergence of harmonic series

–Alternating series test

–Divergence test

–Comparison & limit comparison test

–Integral test

–Absolute & conditional convergence

–Radius and interval of convergence with power series

–Functions expressed as power series

–Taylor and maclaurin series

–Approximating functions with Taylor polynomials and error bounds

Parametric Equations and Polar Coordinates

–Defining curves with parametric equations

–Tangent and concavity of parametric equations

–Area of parametric equations

–Arc length and surface area of parametric equations

–Polar coordinates

–Tangents of polar curves

–Area of polar curves

–Arc length of polar curves

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