MATH 2111 - Calculus III-Multivariable Calculus

Course Description

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 are responsible for purchasing the required materials on their own:

• Stewart, J. (2020). Multivariable Calculus andStudent Solutions Manual. (9th ed.). Cengage Learning.
  Type: Text bundle ISBN: 9780357715093

Note: This bundle can be purchased directly from the publisher's website. A print or fixed-layout version is strongly recommended to ensure alignment with the course materials. 

• For Print Students the study guide, course guide and assignment file are individual files.

Note: The above print files can be purchased through the Wolfie's Campus Store.

Additional requirements

Calculator: Either a scientific calculator or a non-symbolic, graphing calculator is acceptable. Symbolic calculators or calculators with a computer algebra system are not allowed.

Assessments

To successfully complete this course, students must achieve a passing grade of 50% or higher on the overall course and 50% or higher on the mandatory final exam.

Note: The final exam for this course is only available as a in-person exam and must be taken at an approved Testing Centre. Please email exams@tru.ca with any questions.

Recommended requisite(s)

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

Exclusions

MATH 2110