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Calculus 2

Unit 1: Integrals review

Accumulations of change introduction: Integrals reviewApproximation with Riemann sums: Integrals reviewSummation notation review: Integrals reviewRiemann sums in summation notation: Integrals reviewDefining integrals with Riemann sums: Integrals reviewFundamental theorem of calculus and accumulation functions: Integrals review
Interpreting the behavior of accumulation functions: Integrals reviewProperties of definite integrals: Integrals reviewFundamental theorem of calculus and definite integrals: Integrals reviewReverse power rule: Integrals reviewIndefinite integrals of common functions: Integrals reviewDefinite integrals of common functions: Integrals reviewProof videos: Integrals review

Unit 2: Integration techniques

Integrating with u-substitution: Integration techniquesIntegrating using long division and completing the square: Integration techniquesIntegrating using trigonometric identities: Integration techniques
Trigonometric substitution: Integration techniquesIntegration by parts: Integration techniquesIntegrating using linear partial fractions: Integration techniquesImproper integrals: Integration techniques

Unit 3: Differential equations

Differential equations introduction: Differential equationsVerifying solutions for differential equations: Differential equationsSketching slope fields: Differential equationsReasoning using slope fields: Differential equations
Approximation with Euler’s method: Differential equationsSeparation of variables: Differential equationsParticular solutions to differential equations: Differential equationsExponential models: Differential equationsLogistic models: Differential equations

Unit 4: Applications of integrals

Average value of a function: Applications of integralsStraight-line motion: Applications of integralsNon-motion applications of integrals: Applications of integralsArea: vertical area between curves: Applications of integralsArea: horizontal area between curves: Applications of integralsArea: curves that intersect at more than two points: Applications of integralsVolume: squares and rectangles cross sections: Applications of integrals
Volume: triangles and semicircles cross sections: Applications of integralsVolume: disc method (revolving around x- and y-axes): Applications of integralsVolume: disc method (revolving around other axes): Applications of integralsVolume: washer method (revolving around x- and y-axes): Applications of integralsVolume: washer method (revolving around other axes): Applications of integralsArc length: Applications of integralsCalculator-active practice: Applications of integrals

Unit 5: Parametric equations, polar coordinates, and vector-valued functions

Parametric equations intro: Parametric equations, polar coordinates, and vector-valued functionsSecond derivatives of parametric equations: Parametric equations, polar coordinates, and vector-valued functionsArc length: parametric curves: Parametric equations, polar coordinates, and vector-valued functionsVector-valued functions: Parametric equations, polar coordinates, and vector-valued functionsPlanar motion: Parametric equations, polar coordinates, and vector-valued functions
Polar functions: Parametric equations, polar coordinates, and vector-valued functionsArea: polar regions (single curve): Parametric equations, polar coordinates, and vector-valued functionsArea: polar regions (two curves): Parametric equations, polar coordinates, and vector-valued functionsArc length: polar curves: Parametric equations, polar coordinates, and vector-valued functionsCalculator-active practice: Parametric equations, polar coordinates, and vector-valued functions

Unit 6: Series

Convergent and divergent infinite series: SeriesInfinite geometric series: Seriesnth-term test: SeriesIntegral test: SeriesHarmonic series and p-series: SeriesComparison tests: SeriesAlternating series test: SeriesRatio test: SeriesAbsolute and conditional convergence: Series
Alternating series error bound: SeriesTaylor and Maclaurin polynomials intro: SeriesLagrange error bound: SeriesPower series intro: SeriesFunction as a geometric series: SeriesMaclaurin series of eˣ, sin(x), and cos(x): SeriesRepresenting functions as power series: SeriesTelescoping series: SeriesProof videos: Series

Course challenge

Test your knowledge of the skills in this course. Have a test coming up? The Course challenge can help you understand what you need to review.
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