Math101 · Independent Ontario learning library
08 · Subject library
Calculus III
Vectors, partial derivatives, multiple integrals, and calculus in several dimensions.
Start with Arc Length and Curvature →41 complete · 41 total lessons
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Every topic below opens as a full lesson with interactive practice and a printable cheat sheet.
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01Arc Length and CurvatureA rigorous, example-driven guide to arc length and curvature, including hypotheses, method choice, verification, and practice.Full lesson + sheet02Chain Rule in Several VariablesA rigorous, example-driven guide to chain rule in several variables, including hypotheses, method choice, verification, and practice.Full lesson + sheet03Continuity in Several VariablesA rigorous, example-driven guide to continuity in several variables, including hypotheses, method choice, verification, and practice.Full lesson + sheet04Cross ProductThe cross product creates a vector perpendicular to two three-dimensional vectors, with magnitude equal to their parallelogram area.Full lesson + sheet05Curl and DivergenceA rigorous, example-driven guide to curl and divergence, including hypotheses, method choice, verification, and practice.Full lesson + sheet06Derivatives of Vector FunctionsA rigorous, example-driven guide to derivatives of vector functions, including hypotheses, method choice, verification, and practice.Full lesson + sheet07Directional DerivativesA rigorous, example-driven guide to directional derivatives, including hypotheses, method choice, verification, and practice.Full lesson + sheet08Divergence TheoremA rigorous, example-driven guide to divergence theorem, including hypotheses, method choice, verification, and practice.Full lesson + sheet09Dot ProductThe dot product combines two vectors into a scalar that measures directional alignment, angle, projection, and work.Full lesson + sheet10Double IntegralsA rigorous, example-driven guide to double integrals, including hypotheses, method choice, verification, and practice.Full lesson + sheet11Double Integrals in Polar CoordinatesA rigorous, example-driven guide to double integrals in polar coordinates, including hypotheses, method choice, verification, and practice.Full lesson + sheet12Functions of Several VariablesA rigorous, example-driven guide to functions of several variables, including hypotheses, method choice, verification, and practice.Full lesson + sheet13Fundamental Theorem for Line IntegralsA rigorous, example-driven guide to fundamental theorem for line integrals, including hypotheses, method choice, verification, and practice.Full lesson + sheet14GradientA rigorous, example-driven guide to gradient, including hypotheses, method choice, verification, and practice.Full lesson + sheet15Green's TheoremA rigorous, example-driven guide to green's theorem, including hypotheses, method choice, verification, and practice.Full lesson + sheet16Intersections of Lines and PlanesLine-plane and plane-plane intersections are found by combining parametric and scalar equations and interpreting the resulting system.Full lesson + sheet17Iterated IntegralsA rigorous, example-driven guide to iterated integrals, including hypotheses, method choice, verification, and practice.Full lesson + sheet18Lagrange MultipliersA rigorous, example-driven guide to lagrange multipliers, including hypotheses, method choice, verification, and practice.Full lesson + sheet19Limits of Multivariable FunctionsA rigorous, example-driven guide to limits of multivariable functions, including hypotheses, method choice, verification, and practice.Full lesson + sheet20Line IntegralsA rigorous, example-driven guide to line integrals, including hypotheses, method choice, verification, and practice.Full lesson + sheet21Linearization in Several VariablesA rigorous, example-driven guide to linearization in several variables, including hypotheses, method choice, verification, and practice.Full lesson + sheet22Lines in SpaceA rigorous, example-driven guide to lines in space, including hypotheses, method choice, verification, and practice.Full lesson + sheet23Lines in Three DimensionsA line in three-dimensional space is determined by one point and one nonzero direction vector.Full lesson + sheet24Multivariable OptimizationA rigorous, example-driven guide to multivariable optimization, including hypotheses, method choice, verification, and practice.Full lesson + sheet25Parametric SurfacesA rigorous, example-driven guide to parametric surfaces, including hypotheses, method choice, verification, and practice.Full lesson + sheet26Partial DerivativesA rigorous, example-driven guide to partial derivatives, including hypotheses, method choice, verification, and practice.Full lesson + sheet27PlanesA rigorous, example-driven guide to planes, including hypotheses, method choice, verification, and practice.Full lesson + sheet28Planes in Three DimensionsA plane in three-dimensional space is determined by a point and a normal vector perpendicular to every direction in the plane.Full lesson + sheet29Quadric SurfacesA rigorous, example-driven guide to quadric surfaces, including hypotheses, method choice, verification, and practice.Full lesson + sheet30Space CurvesA rigorous, example-driven guide to space curves, including hypotheses, method choice, verification, and practice.Full lesson + sheet31Stokes' TheoremA rigorous, example-driven guide to stokes' theorem, including hypotheses, method choice, verification, and practice.Full lesson + sheet32Surface AreaA rigorous, example-driven guide to surface area, including hypotheses, method choice, verification, and practice.Full lesson + sheet33Surface IntegralsA rigorous, example-driven guide to surface integrals, including hypotheses, method choice, verification, and practice.Full lesson + sheet34Tangent PlanesA rigorous, example-driven guide to tangent planes, including hypotheses, method choice, verification, and practice.Full lesson + sheet35Three-Dimensional Coordinate SystemA rigorous, example-driven guide to three-dimensional coordinate system, including hypotheses, method choice, verification, and practice.Full lesson + sheet36Triple IntegralsA rigorous, example-driven guide to triple integrals, including hypotheses, method choice, verification, and practice.Full lesson + sheet37Triple Integrals in Cylindrical CoordinatesA rigorous, example-driven guide to triple integrals in cylindrical coordinates, including hypotheses, method choice, verification, and practice.Full lesson + sheet38Triple Integrals in Spherical CoordinatesA rigorous, example-driven guide to triple integrals in spherical coordinates, including hypotheses, method choice, verification, and practice.Full lesson + sheet39Vector FieldsA rigorous, example-driven guide to vector fields, including hypotheses, method choice, verification, and practice.Full lesson + sheet40Vector-Valued FunctionsA rigorous, example-driven guide to vector-valued functions, including hypotheses, method choice, verification, and practice.Full lesson + sheet41Vectors in Three DimensionsThree-dimensional vectors extend component methods into space using x-, y-, and z-directions.Full lesson + sheet
