MATH 2111: Calculus III-Multivariable Calculus
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.
Learning outcomes
- 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 topics
- 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 need to source the following on their own:
- Stewart, J. (2016). Multivariable Calculus. (8th ed.) Boston, MA: Cengage Learning.
Type: textbook ISBN: 978-1-305-26664-3
- Clegg, D., Frank, B, (2016). Student Solutions Manual for Multivariable Calculus.
(8th ed.) Boston, MA: Cengage Learning.
Type: textbook ISBN: 978-1-305-27182-1
Additional requirements
Good quality programmable scientific calculator is required.
Assessments
Please be aware that should your course have a final exam, students are responsible for the fee to the online proctoring service, ProctorU, or to the in person approved Testing Centre. Please contact exams@tru.ca with any questions about this.
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 | 6% |
| Assignment 2: Vector Functions | 7% |
| Assignment 3: Partial Differentiation | 8% |
| Assignment 4: Multiple Integrals | 6% |
| Assignment 5: Applications – Triple Integration | 6% |
| Assignment 6: Vector Integration | 7% |
| Final Examination (mandatory) | 60% |
| Total | 100% |
Open Learning Faculty Member Information
An Open Learning Faculty Member is available to assist students. Students will receive the necessary contact information at the start of the course.