Multivariable Calculus

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

• set up and evaluate double and triple integrals over simple regions
• adapt integration problems to different coordinate systems when appropriate and evaluate them
• classify critical points of two variable functions and interpret them geometrically
• evaluate and interpret derivatives of functions of two or more variables
• use line integrals to calculate areas of certain regions

Differentiable calculus of functions of several variables:

• Sketching functions of two variables.
• Limits of multivariable functions.
• Partial derivatives, Gradient, Directional Derivative.
• Tangent plane, Maximum and minimum points.
• Change of variables and the chain rule, Jacobian.
• Second and higher partial derivatives, chain rule for second derivatives.
• Critical points and their classification.
• Lagrange Multipliers.
• Multivariable Taylor Series

Integral calculus of functions of two or three variables:

• Double and repeated integrals, including change of order in a repeated integral.
• General change of variables in a double integral.
• Polar coordinates, cylindrical polar coordinates, spherical polar coordinates.
• Triple integrals in various coordinates.

Line integrals:

• Evaluation of simple line integrals
• The Fundamental Theorem of line integrals
• Green’s Theorem

Lectures, problem classes, workshops, private study

Formative

This is how we’ll give you feedback as you are learning. It is not a formal test or exam.

Individual comments

• Assessment Type: Formative
• Feedback:
• Final Assessment: No
• Group Work: No

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.