Multivariable Calculus

View Resource

Read the Fine Print

Subject:

Mathematics and Statistics

Institution Name:

The Saylor Foundation

Collection:

Saylor Foundation

Grade Level:

Post-secondary

Abstract:

Multivariable Calculus is an expansion of Single-Variable Calculus in that it extends single variable calculus to higher dimensions. This course begins with a fresh look at limits and continuity, moves to derivatives and the process of generalizing them to higher dimensions, and finally examines multiple integrals (integration over regions of space as opposed to intervals). Upon successful completion of this course, the student will be able to: Define and identify vectors; Define and compute dot and cross-products; Solve problems involving the geometry of lines, curves, planes, and surfaces in space; Define and compute velocity and acceleration in space; Define and solve Kepler's Second Law; Define and compute partial derivatives; Define and determine tangent planes and level curves; Define and compute least squares; Define and determine boundaries and infinity; Define and determine differentials and the directional derivative; Define and compute the gradient and the directional derivative; Define, determine, and apply Lagrange multipliers to solve problems; Define and compute partial differential equations; Define and evaluate double integrals; Use rectangular coordinates to solve problems in multivariable calculus; Use polar coordinates to solve problems in multivariable calculus; Use change of variables to evaluate integrals; Define and use vector fields and line integrals to solve problems in multivariable calculus; Define and verify conservative fields and path independence; Define and determine gradient fields and potential functions; Use Green's Theorem to evaluate and solve problems in multivariable calculus; Define flux; Define and evaluate triple integrals; Define and use rectangular coordinates in space; Define and use cylindrical coordinates; Define and use spherical coordinates; Define and correctly manipulate vector fields in space; Evaluate surface integrals and relate them to flux; Use the Divergence Theorem (Gauss' Theorem) to solve problems in multivariable calculus; Define and evaluate line integrals in space; Apply Stokes' Theorem to solve problems in multivariable calculus; Properly apply Maxwell's Equations to solve problems. (Mathematics 103)

Languages:

English

Material Type:

Assessments, Full Course, Homework and Assignments, Lecture Notes, Readings, Syllabi, Textbooks, Video Lectures

Media Format:

Graphics/Photos, Other, Text/HTML, Downloadable docs, Video

Conditions of Use:

Creative Commons Attribution-Noncommercial 3.0
You are welcome to share, remix, and adapt this course under the terms of the Creative Commons Attribution 3.0 Unported License; however, many linked materials within this course are copyright of their respective authors/owners and may not be openly-licensed. Please respect the copyright and terms of use associated with each resource.

Copyright Holder:

The Saylor Foundation