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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:

  1. Stewart, J. (2016). Multivariable Calculus. (8th ed.) Boston, MA: Cengage Learning.
    Type: textbook ISBN: 978-1-305-26664-3
  1. 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.


Please be aware that should your course have a final exam, you are responsible for the fee to the online proctoring service, ProctorU, or to the in-person approved Testing Centre. Please contact 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.

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