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
- solve second order inhomogeneous ODEs
- set up and evaluate double integrals over simple regions
- classify critical points of two variable functions and interpret them geometrically
- evaluate and interpret derivatives of functions of two or more variables
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.A. Adams. Calculus - A Complete course. Addison-Wesley.
R. Wrede & M.R. Spiegel. Advanced Calculus. Schaum.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Coursework | 20% |
| Exam | 80% |
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