|Semester 1 Credit Value:||10|
|MAS1041||Mathematical Methods A|
|MAS1141||Analytical Geometry and the Foundations of Differential Equations|
To introduce students to a variety of analytical and numerical techniques for solving mathematical problems. The relative strengths and weaknesses of different problem-solving techniques will be discussed, enabling students to decide upon the most appropriate method for a given problem. Some basic concepts in mathematical modelling will also be introduced.
Many physical processes can be represented by a mathematical model. These models can tell us a great deal about the system that they describe, provided that the relevant equations can be solved. This module introduces and develops a wide-range of problem solving techniques. Specific examples include methods for finding the roots of equations, methods for solving initial value problems, and the use of integration to find the volumes and surface areas of simple geometrical objects. Although many of these problems are solved using analytical methods, in cases where this is not possible numerical techniques are required. Several useful numerical algorithms will be introduced and implemented using Maple. We shall also discuss several specific examples that explore the more difficult question of how a mathematical model is constructed.
A review of elementary functions, including hyperbolic functions. Numerical methods: Newton-Raphson method, Euler's method, Adams-Bashforth method, Trapezium rule, Simpson's rule, accuracy, implementation using Maple. Applications of integration: arc-lengths, volumes and surfaces of revolution. Suffix notation. Derivatives of vector-valued functions: Cartesian and plane polar coordinates. Mathematical modelling: vector problems (particle dynamics and motion under gravity).
1. know the properties of elementary mathematical functions, including the hyperbolic functions;
2. gain an appreciation for the ways in which integration can be used to determine the arc-length of a curve as well as the volumes and surface areas of simple three-dimensional solids;
3. know how to differentiate vector-valued functions in Cartesian and plane polar coordinates;
4. understand how mathematics can be used to model certain physical phenomena.
1. be able to solve equations involving logarithms, exponentials, trigonometrical functions and hyperbolic functions;
2. be able to use a range of different analytical and numerical techniques to evaluate integrals, locate the roots of equations, and solve first-order initial value problems;
3. be able to implement simple numerical algorithms using Maple
4. be able to use vector-valued functions to solve problems in Newtonian dynamics;
5. be able to determine the most appropriate technique to use in order to solve a given mathematical problem.
|Graduate Skills Framework Applicable:||Yes|
|Scheduled Learning And Teaching Activities||Lecture||26||1:00||26:00||Formal lectures|
|Guided Independent Study||Assessment preparation and completion||4||5:00||20:00||Written assignments|
|Scheduled Learning And Teaching Activities||Lecture||2||1:00||2:00||Revision lectures|
|Scheduled Learning And Teaching Activities||Lecture||4||1:00||4:00||Problem classes|
|Guided Independent Study||Assessment preparation and completion||1||13:00||13:00||Revision for unseen Exam|
|Guided Independent Study||Assessment preparation and completion||1||1:30||1:30||Unseen Exam|
|Guided Independent Study||Assessment preparation and completion||4||2:00||8:00||CBAs|
|Scheduled Learning And Teaching Activities||Practical||3||1:00||3:00||Maple practicals|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||24||0:00||0:00||Office Hours in a staff office|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||4||1:00||4:00||Tutorials in the lecture room|
|Guided Independent Study||Independent study||4||1:00||4:00||Assignment review|
|Guided Independent Study||Independent study||1||14:30||14:30||Studying, practising and gaining understanding of course material|
Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. Practicals are used both for solution of problems and work requiring extensive computation and for simulation to give insight into the ideas/methods studied. Office hours provide an opportunity for more direct contact between individual students and the lecturer.
The format of resits will be determined by the Board of Examiners
|Prob solv exercises||1||M||10||N/A|
A substantial formal unseen examination is appropriate for the assessment of the material in this module. Approximately four written assignments of approximately equal weight (worth approximately 10% in total) and approximately four computer based assessments of approximately equal weight (worth approximately 10% in total) allow the students to develop their problem solving techniques, to practise the methods learnt in the module and to receive feedback; this is thus formative as well as summative assessment.
Disclaimer: The information contained within the Module Catalogue relates to the 2016/17 academic year. In accordance with University Terms and Conditions, the University makes all reasonable efforts to deliver the modules as described. Modules may be amended on an annual basis to take account of changing staff expertise, developments in the discipline, the requirements of external bodies and partners, and student feedback. Module information for the 2017/18 entry will be published here in early-April 2017. Queries about information in the Module Catalogue should in the first instance be addressed to your School Office.