MAU11201 Single-variable calculus
| Module Code | MAU11201 |
|---|---|
| Module Title | Single-variable calculus |
| Semester taught | Semester 1 |
| ECTS Credits | 10 |
| Module Lecturer | Prof. Paschalis Karageorgis |
| Module Prerequisites | N/A |
Assessment Details
- Students are assessed based on 4 homework assignments and each of those contributes 25% towards the overall mark.
- Re-assessment, if needed, consists of 100% exam.
Contact Hours
11 weeks of teaching with 5 lectures and 1 tutorial per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Compute limits and determine whether a given function is continuous or not.
- Determine the intervals on which a given function is increasing/decreasing and concave up/down.
- Use derivatives to solve optimisation problems and related rates problems.
- Integrate functions using the standard techniques of integration.
- Use integrals to compute areas, volumes and length.
- Determine whether a given series converges or not.
Module Content
- Limits and continuity: epsilon-delta definition, Bolzano's theorem, applications.
- Differentiation: Rules of differentiation, mean value theorem, optimisation problems, related rates.
- Integration: Fundamental theorem of calculus, techniques of integration, area, length, volume.
- Sequences and series: Tests for convergence, power series.
Recommended Reading
- Calculus: Early Transcendentals by Anton, Bivens and Davis.
- Calculus by James Stewart.
- Calculus by Michael Spivak.