Module overview
This module extends the ideas of calculus to multiple variables. This is a key step to move towards the formulation of differential equations for complex systems, a core part of modelling in the mathematical sciences.
Aims and Objectives
Learning Outcomes
Learning Outcomes
Having successfully completed this module you will be able to:
- adapt integration problems to different coordinate systems when appropriate and evaluate them
- evaluate and interpret derivatives of functions of two or more variables
- classify critical points of two variable functions and interpret them geometrically
- solve second order inhomogeneous ODEs
- set up and evaluate double integrals over simple regions
Syllabus
• 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.
Learning and Teaching
Teaching and learning methods
Lectures, problem classes, workshops, private study
| Type | Hours |
|---|---|
| Teaching | 48 |
| Independent Study | 102 |
| Total study time | 150 |
Resources & Reading list
Textbooks
R. Wrede & M.R. Spiegel. Advanced Calculus. Schaum.
R.A. Adams. Calculus - A Complete course. Addison-Wesley.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Exam | 80% |
| Coursework | 20% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Exam | 100% |
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.
| Method | Percentage contribution |
|---|---|
| Exam | 100% |
Repeat Information
Repeat type: Internal & External