Multivariable Calculus

This is a complete course in Multivariable calculus. Multivariable calculus is an extension of single variable calculus to calculus with functions of two or more variables. It is expected that anyone taking this course has already knows the basics from single variable calculus: limits and continuity, differentiation and integration.

In this course you will learn how to perform calculus on functions of two or more variables, as well as vector-valued functions. In particular, the topics covered include the basics of three dimensional space and vectors, vector-valued functions including the calculus of vector-valued functions (limits, differentiation, and integration), differentiation of functions of two or more variables, integration of functions of two or more variables, and vector calculus. Single variable Calculus is a prerequisite for this course.

Here is a complete list of the topics that will be covered: Three-dimensional Space and VectorsRectangular Coordinates in 3-spaceVectorsDot ProductCross ProductEquations of LinesEquations of PlanesQuadric SurfacesVector-valued FunctionsArc Length and the TNB-FrameCurvatureFunctions of Multiple Variables and Partial DifferentiationFunctions of Two or More VariablesLimits and ContinuityPartial DerivativesDifferentiabilityChain RuleDirectional DerivativesMaxima and Minima of Functions of Two VariablesMultiple IntegralsDouble Integrals Double Integrals over Nonrectangular RegionsDouble Integrals over Polar RegionsTriple IntegralsCylindrical and Spherical CoordinatesTriple Integrals in Cylindrical and Spherical CoordinatesVector CalculusVector FieldsLine IntegralsIndependence of PathGreen's TheoremParametric SurfacesSurface IntegralsOrientable Surfaces and FluxStoke's TheoremDivergence Theorem.