PHY1115 Mathematical Skills

2007-2008

Code: PHY1115
Title: Mathematical Skills
Instructors: Prof. R. Jones
CATS credits: 20
ECTS credits: 10
Availability: Physics programmes only
Level: 1
Pre-requisites: N/A
Co-requisites: N/A
Background Assumed: N/A
Duration: Semesters I and II
Directed Study Time: 22 tutorials of 1 hours, 10 hours of tests
Private Study Time: 168 hours
Assessment Tasks Time: -
Observation report: 2001/02 MEP (RJ) & AKS (CAGC)

Aims

The module mainly contains material covered in A-level mathematics and is intended to form a sound foundation for the follow-up module PHY1116. The material is largely taught by self-study and is designed to improve understanding of basic mathematics and improve the ability of the student to apply it to problems in the physical sciences and engineering, such as electricity and magnetism (PHY1104) and electronics (PHY1107). The emphasis is on problem solving with examples taken from physics.

Intended Learning Outcomes

Students should be able to:

Module Specific Skills

• demonstrate a factual knowledge of basic mathematics;
• solve problems by selection and application of appropriate methods;

Discipline Specific Skills

• use a text book to self-study and self-evaluate that learning;

Personal and Key Skills

• manage their own learning in order to meet deadlines for completion of work to be discussed in the tutorials;
• discuss problem-solving within a group.

Learning and Teaching Methods

The module will largely involve guided-self study using the recommended core text. Students will work through each topic and answer the questions set. These must be handed in at the start of a weekly tutorial. Credit will be given for participation in the tutorial and completion of these questions. Regular tests following the tutorials monitor progress.

Assignments

Bi-weekly problems sets; Bi-weekly tests.

Assessment

Bi-weekly tests (50%) and a three-hour end-of-semester examination (50%). A credit mark (at most 10% of maximum score for each test) will be given for participation in the earlier tutorial.

Syllabus Plan and Content

1. Algebra
   1. Linear equations
   2. Quadratic equations
2. Trigonometry
3. Binomial Series
4. Differentiation
   1. Elementary differentiation
   2. Further differentiation
5. Integration
   1. Introducing integration
   2. Basic integration
   3. Techniques of integration
6. Vectors
7. Curve sketching
8. Taylor's Thereom
9. Complex Numbers
   1. Introducing complex numbers
   2. Polar representation of complex numbers
   3. Complex algebra and Demoivre's theorm
10. Hyperbolic Functions
11. Differential Equations
    1. Introducing differential equations
    2. Solving first order differential equations
    3. Solving second order differential equations
12. Advanced Topics
    1. Matrices
    2. Non-cartesian co-ordinates

Core Text

Stroud K.A. (2001), Engineering Mathematics (5^th edition), Paulgrave, ISBN 0-333-91939-4 (UL: 510.2462 STR)

Supplementary Text(s)

Lambourne R. and Tinker M. (2000), Basic Mathematics for the Physical Sciences, Wiley, ISBN 0-471-85207-4 (UL: 510.245 LAM)
Lambourne R. and Tinker M. (2000), Further Mathematics for the Physical Sciences, Wiley, ISBN 0-471-86723-3 (UL: In processing)

Formative Mechanisms

Self-monitoring is an integral part of module and the regular bi-weekly tests following the tutorials enables progress to be monitored.

Evaluation Mechanisms

The module will be evaluated using information gathered via the student representation mechanisms, the staff peer appraisal scheme, and measures of student attainment based on summative assessment.