This course takes calculus from the two dimensional world of single variable functions into
the three dimensional world, and beyond, of multivariable functions. Students explore the
following topics: 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.
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.
- Unit 1: Vector geometry, lines and planes in three dimensions
- Unit 2: Vector functions, surfaces in space
- Unit 3: Vector differentiation
- Unit 4: Double integration
- Unit 5: Triple integration
- Unit 6: Vector integration
Required text and materials
Students will receive the following:
- Stewart, James. (2016). Multivariable Calculus. 8th edition. Brooks
Textbook, ISBN: 9781305266643
- Stewart, James. (2016). Student Solutions Manual for Multivariable Calculus. 8th
edition. Brooks Cole.
Textbook, ISBN: 9781305271821
Good quality programmable scientific calculator is required.
Please be aware that due to COVID-19 safety guidelines all in-person exams have been suspended. As such, all final exams are currently being delivered through ProctorU, which has an approximate fee of $35 involved. There will be more information in your course shell, on how to apply, if your course has a final exam.
To successfully complete this course, students must achieve 50% or higher on the overall
course, and 50% or higher on the final mandatory examination.
|Assignment 1: Vectors and the Geometry of Space
|Assignment 2: Vector Functions
|Assignment 3: Partial Differentiation
|Assignment 4: Multiple Integrals
|Assignment 5: Applications – Triple Integration
|Assignment 6: Vector Integration
|Final Examination (mandatory)
Open Learning Faculty Member
An Open Learning Faculty Member is available to assist students. Students will receive the necessary contact information at the start of your course.