MATH 2111
Calculus III-Multivariable Calculus

3.0 Credits

Description

This course takes calculus from the two dimensional world of single variable functions into the three dimensional world, and beyond, of multivariable functions. Topics include the following: vector geometry and the analytic geometry of lines, planes and surfaces; calculus of curves in two or three dimensions, including arc length and curvature; calculus of scalar-valued functions of several variables, including the gradient, directional derivatives and the Chain Rule; Lagrange multipliers and optimization problems; double integrals in rectangular and polar coordinates; triple integrals in rectangular, cylindrical and spherical coordinates; calculus of vector fields including line integrals, curl and divergence, fundamental theorem for line integrals and Green's theorem.

Delivery Method

Print-based or Web-based.

Prerequisites

Two courses in differential and integral calculus, such as MATH 1141 and 1241 are strongly recommended. Students should have done well in these courses in order to succeed in this difficult course.

Objectives

Upon successful completion of this course, students should be able to:

  • Handle vectors fluently in solving problems involving the geometry of lines, curves, planes, and surfaces in space.
  • Visualize and draw graphs of surfaces in space.
  • Differentiate scaler functions of vectors.
  • Integrate vectors.
  • Calculate extreme values using Lagrange multipliers.
  • Solve double and triple integrals.
  • Translate real-life situations into the symbolism of mathematics and find solutions for the resulting models.

Course Outline

Topics

  1. Vector geometry, lines and planes in three dimensions
  2. Vector functions, surfaces in space
  3. Vector differentiation
  4. Double integration
  5. Triple integration
  6. Vector integration

Maximum Completion

30 weeks.

Required Text and Materials

  1. Stewart, James. Multivariable Calculus. 7th edition. Brooks Cole, 2011.
    Type: Textbook, ISBN: 9780538497879 / 0538497874
  1. Stewart, James. Student Solutions Manual for Multivariable Calculus. 7th edition. Brooks Cole, 2011.
    Type: Textbook, ISBN: 9780840049452 / 0840049455

Additional Requirements

Good quality programmable scientific calculator is required.

Open Learning Faculty Member Information

An Open Learning Faculty member is available to assist students. Primary communication is by phone if you are taking the print version of the course and through Blackboard's "Mail" tool if you are taking the web version. You will receive the necessary contact information when you start your course.

Assessment

Assignment 1 6%
Assignment 2 7%
Assignment 3 8%
Assignment 4 6%
Assignment 5 6%
Assignment 6 7%
Final exam 60%
Total 100%

In order to successfully complete this course, you must obtain at least 50% on the final mandatory examination and 50% overall. Students who do not submit an assignment will be assigned a mark of zero (0) for that assignment. It is recommended that students complete all assignments in order to achieve the learning outcomes of the course.