
Calculus
9-12
Course Outline
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Limits
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Introduction to Calculus – Limits
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Finding limits from graphs
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Continuity
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Finding limits algebraically – direct substitution
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Finding limits algebraically – when direct substitution is not possible
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Infinite limits – vertical asymptotes
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Limits at infinity – horizontal asymptotes
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Intermediate value theorem
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Squeeze theorem
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Limit laws
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Derivatives
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Definition of derivative
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Estimating Derivatives from a table
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Power rule
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Slope and equation of tangent line
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Chain rule
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Derivative of trigonometric functions
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Derivative of exponential functions
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Product rule
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Quotient rule
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Implicit differentiation
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Derivative of inverse trigonometric functions
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Derivative of logarithmic functions
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Higher order derivatives
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Derivative Applications
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Position velocity acceleration
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Critical number & maximum and minimum values
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L’Hospital’s rule
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Curve sketching
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Optimization
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Related rates
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Rolle’s Theorem
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Mean value theorem
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Linear approximation
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Quadratic approximation
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Demand, revenue, cost & profit
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Marginal revenue, and maximizing revenue & average revenue
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Marginal cost, and minimizing cost & average cost
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Marginal profit, and maximizing profit & average profit
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Elasticity of demand
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Integrals
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Antiderivatives
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Riemann sum
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Definite integral
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Fundamental theorem of calculus
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Integration techniques
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U-Substitution
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Integration by parts
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Integration using trigonometric identities
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Trigonometric substitution
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Integration of rational functions by partial fractions
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Improper integrals
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Numerical integration
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Integration Applications
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Areas between curves
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Volumes of solid with known cross-sections
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Volumes of solids of revolution – Disk method
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Volumes of solids of revolution – Shell method
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Average value of a function
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Arc length
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Consumer and producer surplus
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Continuous money flow
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Differential Equations
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Order and solutions to differential equations
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Separable equations
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Modeling with differential equations
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Sequence and Series
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Introduction to sequences
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Monotonic and bounded sequences
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Introduction to infinite series
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Convergence and divergence of normal infinite series
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Convergence & divergence of geometric series
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Convergence & divergence of telescoping series
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Divergence of harmonic series
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p Series
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Alternating series test
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Divergence test
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Comparison & limit comparison test
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Integral test
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Ratio test
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Root test
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Absolute & conditional convergence
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Radius and interval of convergence with power series
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Functions expressed as power series
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Taylor series and Maclaurin series
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Approximating functions with Taylor polynomial and error bounds
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Parametric Equations and Polar Coordinates
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Defining curves with parametric equations
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Tangent and concavity of parametric equations
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Area of parametric equations
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Arc length and surface area of parametric equations
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Polar coordinates
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Tangents of polar curves
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Area of polar curves
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Arc length of polar curves