MAU11E01 Engineering mathematics I
| Module Code | MAU11E01 |
|---|---|
| Module Title | Engineering mathematics I |
| Semester taught | Semester 1 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Patrick Fritzsch |
| Module Prerequisites | N/A |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 1.
- Continuous assessment contributes 20% towards the overall mark.
- Re-assessment, if needed, consists of 100% exam.
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
- Recognise mathematical structures in practical problems, translate these problems into mathematical language, and then analyse them using methods from single-variable calculus.
- Use derivatives to find the minimum and maximum values of a function of one real variable.
- Compute definite integrals using a variety of methods of integration.
- Use integrals to compute various physical quantities such as volume, area and length.
Module Content
- Functions: domain and range, operations with functions, inverse function, algebraic function, rational and trigonometric functions.
- Limits and continuity: limits and one-sided limits, limits at infinity, asymptotes, continuity, intermediate value property.
- Differentiation: definition of derivative, rules of differentiation, implicit differentiation, linear approximation.
- Applications of derivatives: graphs of functions, optimisation problems, related rates, Newton-Raphson method.
- Integration: definite integral, Riemann sums, antiderivatives, integration by substitution, fundamental theorem of calculus.
- Applications of integrals: area between two curves, volumes and areas of solids of revoution, length of a plane curve.
Recommended Reading
- Calculus: Late transcendentals by Anton, Bivens and Davis.