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Calculus Topics

Limits

Introduction to Calculus - Limits
Finding limits from graphs
Continuity
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
Limit laws

Derivatives

Definition of derivative
Power rule
Slope and equation of tangent line
Chain rule
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
Riemann sum
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 solid with known cross-sections
Volumes of solids of revolution - Disc method
Volumes of solid of revolution - Shell method
Average value of a function
Arc length
Consumer and producer surplus
Continuous money flow

Differential Equations

Order and solutions to differential equations
Separable equations
Modeling with 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
P Series
Alternating series test
Divergence test
Comparison & limit comparison test
Integral test
Ratio test
Root test
Absolute & conditional convergence
Radius and interval of convergence with power series
Functions expressed as power series
Taylor series 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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