Double Integrals
Triple Integrals
Differential equations introduction: Differential equationsv
Verifying solutions for differential equations: Differential equations
Sketching slope fields: Differential equations
Reasoning using slope fields: Differential equations
Approximation with Euler’s method: Differential equations
Separation of variables: Differential equations
Particular solutions to differential equations: Differential equations
Exponential models: Differential equations
Logistic models
Average value of a function: Applications of integrals
Straight-line motion: Applications of integrals
Non-motion applications of integrals: Applications of integrals
Area: vertical area between curves: Applications of integrals
Area: horizontal area between curves: Applications of integrals
Area: curves that intersect at more than two points: Applications of integrals
Volume: squares and rectangles cross sections: Applications of integrals
Volume: triangles and semicircles cross sections: Applications of integrals
Volume: disc method (revolving around x- and y-axes): Applications of integrals
Volume: disc method (revolving around other axes): Applications of integrals
Volume: washer method (revolving around x- and y-axes): Applications of integrals
Volume: washer method (revolving around other axes): Applications of integrals
Arc length: Applications of integrals
Calculator-active practice
Parametric equations intro: Parametric equations, polar coordinates, and vector-valued functions
Second derivatives of parametric equations: Parametric equations, polar coordinates, and vector-valued functions
Arc length: parametric curves: Parametric equations, polar coordinates, and vector-valued functions
Vector-valued functions: Parametric equations, polar coordinates, and vector-valued functions
Planar motion: Parametric equations, polar coordinates, and vector-valued functions
Polar functions: Parametric equations, polar coordinates, and vector-valued functions
Area: polar regions (single curve): Parametric equations, polar coordinates, and vector-valued functions
Area: polar regions (two curves): Parametric equations, polar coordinates, and vector-valued functions
Arc length: polar curves: Parametric equations, polar coordinates, and vector-valued functions
Calculator-active practice
Convergent and divergent infinite series: Series
Infinite geometric series: Series
nth-term test: Series
Integral test: Series
Harmonic series and p-series: Series
Comparison tests: Series
Alternating series test: Series
Ratio test:
Absolute and conditional convergence: Series
Alternating series error bound: Series
Taylor and Maclaurin polynomials intro: Series
Lagrange error bound: Series
Power series intro: Series
Function as a geometric series: Series
Maclaurin series of eˣ, sin(x), and cos(x): Series
Representing functions as power series: Series
Telescoping series: Series
Triple Integrals
Differential equations introduction: Differential equationsv
Verifying solutions for differential equations: Differential equations
Sketching slope fields: Differential equations
Reasoning using slope fields: Differential equations
Approximation with Euler’s method: Differential equations
Separation of variables: Differential equations
Particular solutions to differential equations: Differential equations
Exponential models: Differential equations
Logistic models
Average value of a function: Applications of integrals
Straight-line motion: Applications of integrals
Non-motion applications of integrals: Applications of integrals
Area: vertical area between curves: Applications of integrals
Area: horizontal area between curves: Applications of integrals
Area: curves that intersect at more than two points: Applications of integrals
Volume: squares and rectangles cross sections: Applications of integrals
Volume: triangles and semicircles cross sections: Applications of integrals
Volume: disc method (revolving around x- and y-axes): Applications of integrals
Volume: disc method (revolving around other axes): Applications of integrals
Volume: washer method (revolving around x- and y-axes): Applications of integrals
Volume: washer method (revolving around other axes): Applications of integrals
Arc length: Applications of integrals
Calculator-active practice
Parametric equations intro: Parametric equations, polar coordinates, and vector-valued functions
Second derivatives of parametric equations: Parametric equations, polar coordinates, and vector-valued functions
Arc length: parametric curves: Parametric equations, polar coordinates, and vector-valued functions
Vector-valued functions: Parametric equations, polar coordinates, and vector-valued functions
Planar motion: Parametric equations, polar coordinates, and vector-valued functions
Polar functions: Parametric equations, polar coordinates, and vector-valued functions
Area: polar regions (single curve): Parametric equations, polar coordinates, and vector-valued functions
Area: polar regions (two curves): Parametric equations, polar coordinates, and vector-valued functions
Arc length: polar curves: Parametric equations, polar coordinates, and vector-valued functions
Calculator-active practice
Convergent and divergent infinite series: Series
Infinite geometric series: Series
nth-term test: Series
Integral test: Series
Harmonic series and p-series: Series
Comparison tests: Series
Alternating series test: Series
Ratio test:
Absolute and conditional convergence: Series
Alternating series error bound: Series
Taylor and Maclaurin polynomials intro: Series
Lagrange error bound: Series
Power series intro: Series
Function as a geometric series: Series
Maclaurin series of eˣ, sin(x), and cos(x): Series
Representing functions as power series: Series
Telescoping series: Series