MAU11202 Advanced calculus
| Module Code | MAU11202 |
|---|---|
| Module Title | Advanced calculus |
| Semester taught | Semester 2 |
| ECTS Credits | 5 |
| Module Lecturer | |
| Module Prerequisites | MAU11201 Single-variable calculus |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 2.
- Continuous assessment contributes 20% towards the overall mark.
- Any failed components are reassessed, if necessary, by an exam in the reassessment session.
Contact Hours
11 weeks of teaching with 3 lectures and 1 tutorial per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Analyse the behaviour of functions of several variables, present the result graphically, and calculate partial derivatives of functions of several variables including those which are defined implicitly.
- Obtain equations for tangent lines to plane curves and tangent planes to surfaces.
- Apply derivative tests and the method of Lagrange multipliers to find maxima and minima of functions of several variables, both local and global.
- Compute multiple integrals, in both Cartesian and polar coordinates, and thus compute areas, volumes and centres of mass.
Module Content
- Vector-valued functions: parametric curves, calculus, change of parameter.
- Partial derivatives: definition, chain rule, gradients, maxima and minima.
- Multiple integrals: double and triple integrals, surface area.