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:
- classify critical points of two variable functions and interpret them geometrically
- set up and evaluate double and triple integrals over simple regions
- evaluate and interpret derivatives of functions of two or more variables
- use line integrals to calculate areas of certain regions
- adapt integration problems to different coordinate systems when appropriate and evaluate them
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 |
---|---|
Teaching | 54 |
Independent Study | 96 |
Total study time | 150 |
Resources & Reading list
Textbooks
ADAMS R.A.. Calculus - A Complete course. Addison-Wesley.
WREDE R. & SPIEGEL, M.R. Advanced Calculus. Schaum.
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