School of Mathematics and Statistics (SoMaS)

## 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

## 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.

1. Solving equations
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.