Module overview
This module introduces the main ideas and techniques of differential and integral calculus of functions of two or more variables.
One of the pre-requisites for MATH2003, MATH2011, MATH2014, MATH3033, MATH2038, MATH2039, MATH2045 and MATH2040
Linked modules
Pre-requisites: MATH1048 AND MATH1059
Aims and Objectives
Learning Outcomes
Learning Outcomes
Having successfully completed this module you will be able to:
- evaluate and interpret derivatives of functions of two or more variables
- adapt integration problems to different coordinate systems when appropriate and evaluate them
- classify critical points of two variable functions and interpret them geometrically
- use line integrals to calculate areas of certain regions
- set up and evaluate double and triple integrals over simple regions
Syllabus
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
Learning and Teaching
Teaching and learning methods
Lectures, problem classes, workshops, private study
| Type | Hours |
|---|---|
| Independent Study | 96 |
| Teaching | 54 |
| Total study time | 150 |
Resources & Reading list
Textbooks
WREDE R. & SPIEGEL, M.R. Advanced Calculus. Schaum.
ADAMS R.A.. Calculus - A Complete course. Addison-Wesley.
Assessment
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.
| Method | Percentage contribution |
|---|---|
| Written exam | 80% |
| Homework Exercises | 20% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Written 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 |
|---|---|
| Written exam | 100% |
Repeat Information
Repeat type: Internal & External