PHY1025 Mathematics Skills 2017-18
Prof. G.P. Srivastava
 
Delivery Weeks: T1:01-05,07-12
Level: 4 (NQF)
Credits: 15 NICATS / 7.5 ECTS
Enrolment: 149 students (approx)

Description

All physicists must possess a sound grasp of mathematical methods and a good level of 'fluency' in their application. This module covers areas such as differential calculus, complex numbers, and matrices that have wide applicability throughout physics. It provides a firm foundation on which the follow-up module PHY1026 Mathematics II will build, and emphasises problem solving with examples taken from physical sciences.

Module Aims

This module pre-dates the current template; refer to the description above and the following ILO sections.

Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

Syllabus Plan

  1. Foundation Mathematics (Preliminary Self-Study and Self-Evaluation Pack)
    1. Algebra
    2. Trigonometric functions
    3. Trigonometry and the binomial theorem
    4. Methods of differentiation and integration
    5. Curve sketching
  2. Matrices
    1. Matrix addition, subtraction, multiplication
    2. Inversion of matrices
    3. Applications to the solution of systems of homogeneous and inhomogeneous linear equations
    4. Evaluating numerical determinants
    5. Introduction to eigenvalues and eigenvectors
  3. Calculus with a Single Variable
    1. Advanced methods of Differentiation
    2. Advanced methods of Integration
  4. Calculus with Several Variables
    1. Partial differentiation, the differential, Reciprocal and Reciprocity Theorems, total derivatives of implicit functions, higher order partial derivatives
    2. Coordinate systems in 2- and 3-dimensional geometries - Cartesian, plane-polar, cylindrical and spherical polar coordinate systems
    3. Two-dimensional and three-dimensional integrals and their application to finding volumes and masses
    4. Line integrals: parametrisation; work as a line integral
  5. Series Expansions, Limits and Convergence
    1. Taylor and Maclaurin series, expansions of standard functions
  6. Complex Numbers
    1. Argand diagram, modulus-argument form, exponential form, de Moivre's theorem
    2. Trigonometric functions
    3. Hyperbolic functions

Learning and Teaching

Learning Activities and Teaching Methods

Description Study time KIS type
22×1-hour lectures 22 hours SLT
5×3-hour self-study packages 15 hours GIS
5×3-hour problems sets 15 hours GIS
3×5-hour problems sets 15 hours GIS
Problems class support 11 hours SLT
Tutorial support 3 hours SLT
Reading, private study and revision 69 hours GIS

Assessment

Weight Form Size When ILOS assessed Feedback
0% Exercises set by tutor 3×1-hour sets (typical) Scheduled by tutor 1-9 Discussion in tutorials
0% Guided self-study 5×6-hour packages Fortnightly 1-9 Discussion in tutorials
20% 8 × Problems Sets 30 hours total Weekly 1-9 Marked in problems class, then discussed in tutorials
15% Mid-term Test 1 30 minutes Weeks T1:04 1-9 Marked, then discussed in tutorials
15% Mid-term Test 2 30 minutes Weeks T1:09 1-9 Marked, then discussed in tutorials
50% Final Examination 120 minutes January 1-9 Mark via MyExeter, collective feedback via ELE and solutions.

Resources

The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

Supplementary texts:

ELE:

Further Information

Prior Knowledge Requirements

Pre-requisite Modules none
Co-requisite Modules none

Re-assessment

Re-assessment is not available except when required by referral or deferral.

Original form of assessment Form of re-assessment ILOs re-assessed Time scale for re-assessment
Whole module Written examination (100%) 1-9 August/September assessment period

Notes: See Physics Assessment Conventions.

KIS Data Summary

Learning activities and teaching methods
SLT - scheduled learning & teaching activities 36 hrs
GIS - guided independent study 114 hrs
PLS - placement/study abroad 0 hrs
Total 150 hrs
Summative assessment
Coursework 20%
Written exams 80%
Practical exams 0%
Total 100%

Miscellaneous

IoP Accreditation Checklist
  • MT-01 Trigonometric functions.
  • MT-02 Hyperbolic functions.
  • MT-04 Series expansions, limits and convergence.
  • MT-11 Matrices to the level of eigenvalues and eigenvectors.
Availability unrestricted
Distance learning NO
Keywords Physics; Algebra; Calculus; Complex numbers; Differentiation; Equations; Functions; Integration; Matrices; Series.
Created 01-Oct-10
Revised 01-Oct-11