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Master derivatives, integrals, and advanced applications
Aligned with AP exam and College Board requirements
Most students improve one letter grade in 4-6 weeks
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Finding limits from graphs
Limit laws
Finding limits algebraically - direct substitution
Finding limits algebraically - when direct substitution is not possible
Squeeze theorem
l'Hospital's rule
Infinite limits - vertical asymptotes
Continuity
Intermediate value theorem
Definition of derivative
Estimating derivatives from a table
Power rule
Chain rule
Derivative of trigonometric functions
Derivative of exponential functions
Derivative of logarithmic functions
Product rule
Quotient rule
Derivative of inverse trigonometric functions
Implicit differentiation
Higher order derivatives
Slope and equation of tangent line
Critical number & maximum and minimum values
Tangents and concavity of parametric equations
Tangents of polar curves
Curve sketching
Mean value theorem
Rectilinear motion: Derivative
Related rates
Optimization
Antiderivatives
Riemann sum
Definite integral
Fundamental theorem of calculus
Improper integrals
U-Substitution
Integration using trigonometric identities
Trigonometric substitution
Integration by parts
Integration of rational functions by partial fractions
Average value of a function
Areas between curves
Area of polar curves
Volumes of solids with known cross-sections
Volumes of solids of revolution - Disc method
Volumes of solids of revolution - Shell method
Arc length and surface area of parametric equations
Arc length of polar curves
Introduction to differential equations
Separable equations
Slope fields
Euler's method
Introduction to sequences
Introduction to infinite series
Convergence and divergence of normal infinite series
Convergence and divergence of geometric series
Divergence of harmonic series
P Series
Alternating series test
Divergence test
Comparison and limit comparison test
Integral test
Ratio test
Absolute and 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
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