What you'll learn
Calculus in 3-space
Partial Differentiation
Multiple Integration
Vector Calculus
Requirements
Single Variable Calculus
Description
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 Vectors
Rectangular Coordinates in 3-space
Vectors
Dot Product
Cross Product
Equations of Lines
Equations of Planes
Quadric Surfaces
Vector-valued Functions
Arc Length and the TNB-Frame
Curvature
Functions of Multiple Variables and Partial Differentiation
Functions of Two or More Variables
Limits and Continuity
Partial Derivatives
Differentiability
Chain Rule
Directional Derivatives
Maxima and Minima of Functions of Two Variables
Multiple Integrals
Double Integrals
Double Integrals over Nonrectangular Regions
Double Integrals over Polar Regions
Triple Integrals
Cylindrical and Spherical Coordinates
Triple Integrals in Cylindrical and Spherical Coordinates
Vector Calculus
Vector Fields
Line Integrals
Independence of Path
Green's Theorem
Parametric Surfaces
Surface Integrals
Orientable Surfaces and Flux
Stoke's Theorem
Divergence Theorem
Who this course is for
Students that want to learn Multivariable Calculus and Vector Analysis
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