PHY1015 Mathematics I

1999-2000

Code: PHY1015
Title: Mathematics I
Instructors: Dr A.K. Savchenko and Prof. R. Jones
HE credits: 20
ECTS credits: 10
Availability: unrestricted
Level: 1
Prerequisites: none
Corequisites: none
Background Assumed: none
Duration: Semester I
Directed Study: 11 tutorials of 2 hours, 10 hours of tests
Private Study: 168 hours
Supports Programme Aims: 1, 5, 7 and 8
Supports Programme Objectives: none

Assessment Methods

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 attendance at the earlier tutorial.

Rationale

The module mainly contains material covered in A-level mathematics. The material is largely self-taught 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 (PHY1004) and electronics (PHY1007). The emphasis is on problem solving with examples taken from physics.

Intended Learning Outcomes

A knowledge of basic mathematics demonstrated by the ability to solve problems involving, for example, real and complex numbers, series, trigonometical formulae, differential and integral calculus, vectors and Taylor series.

Teaching and Learning Methods

The module will be largely self-taught, with about 25 module components from the FLAP (Flexible Learning Approach to Physics) teaching resource distributed in weeks 1 to 10. Each module component consists of a fast track and a normal track, a module-component summary, and an exit test. The fast track is first worked through and then the exit test attempted. If difficulties arise, the normal track is worked through. The exit questions are worked through and the solutions inspected in the weekly tutorials. Regular weekly tests following the tutorials monitor progress.

Transferable Skills

The structure of the course engenders appreciable self-study skills. and reinforce a knowledge of basic mathematics. Students are required to meet deadlines for completion of work to be discussed in the tutorials and must therefore develop appropriate time-management strategies.

Assignments

Working through self-study packs; weekly tests.

Module Text

Not applicable

Supplementary Reading

Not applicable

Syllabus Plan and Content

Note: Each student will be charged £15 as a contribution to the cost of copying the several hundred pages covering the module components. This should be paid into the Accounts Office (room 605) by the end of week 2.

1. Algebra and functions
   1. M1.5 Exponential and logarithmic functions
   2. M1.6 Trigonometric functions
   3. M1.7 Series expansions and approximations
2. Vectors and geometry
   1. M2.1 Introducing geometry
   2. M2.2 Introducing co-ordinate geometry
   3. M2.4 Introducing scalars and vectors
   4. M2.5 Working with vectors
   5. M2.6 The scalar product of vectors
   6. M2.7 The vector product of vectors
3. Complex numbers
   1. M3.1 Introducing complex numbers
   2. M3.2 Polar representation of complex numbers
   3. M3.3 Complex algebra and Demoivre's theorm
4. Differentiation
   1. M4.1 Introducing differentiation
   2. M4.2 Basic differentiation
   3. M4.3 Further differentiation
   4. M4.5 Taylor expansions and polynomial approximations
   5. M4.4 Stationary points and graphing
   6. M4.6 Hyperbolic functions and differentiation
5. Integration
   1. M5.1 Introducing integration
   2. M5.2 Basic integration
   3. M5.3 Techniques of integration
6. Differential equations
   1. M6.1 Introducing differential equations
   2. M6.2 Solving first order differential equations
   3. M6.3 Solving second order differential equations

Feedback to Students

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

Feedback from Students

Feedback from students on the module is gathered via the standard student representation mechanisms.