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

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 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 receive the following:

  1. Stewart, James. (2016). Multivariable Calculus. 8th edition. Brooks Cole.
    Textbook, ISBN: 9781305266643
  1. Stewart, James. (2016). Student Solutions Manual for Multivariable Calculus. 8th edition. Brooks Cole.
    Textbook, ISBN: 9781305271821

Additional requirements

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 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

An Open Learning Faculty Member is available to assist students. Students will receive the necessary contact information at the start of your course.

Search To Top