MAS100 Mathematics with Maple
| Semester 1, 2011/12 | 10 Credits | ||||
| Lecturer: | Dr Simon Willerton | Home page | Timetable | Reading List | |
| Aims | Outcomes | Teaching Methods | Assessment | Full Syllabus | |
In this course we learn to use a program called Maple, which is a very powerful tool for solving problems in mathematics. Maple will also be used, to varying extents, in many subsequent courses. In parallel with learning Maple, we will review and extend some topics from A-level. Using Maple we will be able to treat complex examples painlessly, look systematically for patterns, visualize our results graphically, and so gain new insights.
Prerequisites: A-level mathematics (or equivalent)
The following modules have this module as a prerequisite:
| MAS101 | Probability, Sets and Complex Numbers |
| MAS103 | Differential and Difference Equations |
| MAS104 | Foundations of Probability and Statistics |
| MAS105 | Numbers and Proofs |
| MAS112 | Vectors and Mechanics |
| MAS170 | Practical Calculus |
| MAS171 | Matrices and Geometry |
| MAS174 | Applications of Probability and Statistics |
| MAS175 | Groups and Symmetries |
Outline syllabus
- Introduction to Maple
- Solving equations
- Special functions
- Differentiation
- Integration
- Taylor series
Aims
- Learn to use Maple to solve and visualise mathematical problems.
- Investigate mathematical phenomena experimentally, and learn how to report conclusions in a coherent way.
- Revise and extend A-level topics (including algebraic manipulation, properties of special functions, differentiation and integration) with new perspectives provided by Maple
Learning outcomes
Teaching methods
Each week, students will attend one lecture, one lab session, and one tutorial. Some lectures will cover aspects of Maple, but most learning of Maple will take place in the lab sessions. In tutorials, students will work on problems by hand.
11 lectures, 11 tutorials, 11 practicals
Assessment
20% for online tests (roughly 1 per week); 80% for the final exam (2 hours, about 20 questions, all questions compulsory).
Full syllabus
0. Introduction to Maple
Simple examples of the main capabilities of Maple.
Expansion, factoring, collection of similar terms, simplification of
algebraic fractions.
Plotting graphs, controlling scales and axes, combining plots.
Polar coordinates and curves given parametrically.
Graphical solution of various problems.
Various methods of solution, by hand or using Maple. Symbolic and numerical solutions. Problems with no solutions or many solutions. Using solutions in further calculations. 2. Special functions
Exponentials and logarithms. Trigonometric and hyperbolic functions. Identities between such functions, and how to prove them. 3. Differentiation
The geometric and numerical meaning of differentiation. Derivatives of some standard functions. Rules for calculating derivatives. Implicit derivatives and higher-order derivatives. 4. Integration
The meaning of integration. Integrals of some standard functions. Methods for finding integrals (by parts and by substitution). 5. Taylor series
Approximation by polynomials and the relation with higher derivatives. Calculation of Taylor series.
Reading list
| Type | Author(s) | Title | Library | Blackwells | Amazon |
|---|---|---|---|---|---|
| B | Cheung | Getting started with Maple | 510.285(C) | Blackwells | Amazon |
(A = essential, B = recommended, C = background.)
Most books on reading lists should also be available from the Blackwells shop on Mappin Street.
Timetable
| - | |||||||
| Fri | 13:00 - 13:50 | lab session | (group 6) | Hicks Room G39a |