MA2001: Calculus of Several Variables
| School | Cardiff School of Mathematics |
| Department Code | MATHS |
| Module Code | MA2001 |
| External Subject Code | 100405 |
| Number of Credits | 10 |
| Level | L5 |
| Language of Delivery | English |
| Module Leader | Dr Matthew Dawes |
| Semester | Autumn Semester |
| Academic Year | 2022/3 |
Outline Description of Module
This module will be dedicated to transferring all basic notions of calculus of functions of one variable to functions of several variables including limits, continuity, extrema, differentiation and integration. Additionally, the students will learn basic ideas about curves and surfaces.
On completion of the module a student should be able to
- Locate points of discontinuity of specified functions
- Find equations for tangent planes to surfaces
- Expand functions of two variables in Taylor Series
- Locate stationary points of functions of two variables
- Determine the nature of stationary points
- Determine maximum and minimum values of functions subject to constraints
- Evaluate double and triple integrals by expressing them as repeated integrals and by change of variable
- Understand the proofs of the theorems underlying the procedures described in the course.
How the module will be delivered
Modules will be delivered through blended learning. You will be guided through learning activities appropriate to your module, which may include:
- Weekly face to face classes (e.g. labs, lectures, exercise classes)
- Electronic resources that you work through at your own pace (e.g. videos, exercise sheets, lecture notes, e-books, quizzes)
Students are also expected to undertake self-guided study throughout the duration of the module.
Skills that will be practised and developed
Skills:
Understand and apply the methods of differential and integral calculus to problems involving more than one variable.
Transferable Skills:
Formulating and solving problems by means of a suitable previously understood apparatus.
Assessment Breakdown
| Type | % | Title | Duration(hrs) |
|---|---|---|---|
| Exam - Autumn Semester | 90 | Calculus Of Several Variables | 2 |
| Written Assessment | 5 | Coursework 1 | N/A |
| Written Assessment | 5 | Coursework 2 | N/A |
Syllabus content
- Functions of two and more variables
- Limits and continuity.
- Partial derivatives and differentiability.
- Tangent plane.
- Chain rule.
- Taylor’s theorem.
- Maxima and Minima
- Stationary points of functions.
- Classification of stationary points
- Constraints and Lagrange multipliers.
- Multiple integration
- Double and Triple integrals.
- Reduction to iterated integrals.
- Change of variables.
- Jacobians and their properties.
- Plane-polar coordinates.
- Cylindrical and spherical polar coordinates.