Calculus II

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

• classify critical points of two variable functions and interpret them geometrically
• solve second order inhomogeneous ODEs
• evaluate and interpret derivatives of functions of two or more variables
• adapt integration problems to different coordinate systems when appropriate and evaluate them
• set up and evaluate double integrals over simple regions

• Solution of second order inhomogeneous ODEs.
• Variation of parameters
• Boundary value problems
• 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.
• Polar coordinates.
• Second and higher partial derivatives, chain rule for second derivatives.
• Critical points and their classification.
• Lagrange Multipliers.
• Multivariable Taylor Series
• Double and repeated integrals, including change of order in a repeated integral.

Lectures, problem classes, workshops, private study

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.