| PHY1025 |
Mathematics Skills |
2013-14 |
|
Dr P.G. Petrov |
|
| |
| Delivery Weeks: |
T1:01-05,07-12 |
|
| Level: |
4 (NQF) |
|
| Credits: |
15 NICATS / 7.5 ECTS |
|
| Enrolment: |
144 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:
-
Module Specific Skills and Knowledge:
- make efficient use of the techniques and concepts of foundation-level
mathematics: algebra, trigonometry and calculus;
- make series expansions of simple functions and determine
their asymptotic behaviour;
- perform basic arithmetic and algebra with complex numbers;
- perform basic operations on matrices and solve systems of
simultaneous linear equations;
- evaluate single, double and triple integrals in straightforward cases;
- evaluate partial derivatives;
-
Discipline Specific Skills and Knowledge:
- tackle, with facility, mathematically formed problems and their solution;
-
Personal and Key Transferable / Employment Skills and Knowledge:
- work co-operatively and use peer group as a learning resource;
- develop appropriate time-management strategies and meet deadlines for completion of work.
Syllabus Plan
-
Foundation Mathematics (Self-Study Pack)
- Algebra
- Trigonometric functions
- Trigonometry and the binomial theorem
-
Matrices
- Matrix addition, subtraction, multiplication
- Inversion of matrices
- Applications to the solution of systems of homogeneous and inhomogeneous linear equations
- Evaluating numerical determinants
- Introduction to eigenvalues and eigenvectors
-
Calculus with a Single Variable
- Differentiation
- Integration I
- Integration II
-
Calculus with Several Variables
- Partial differentiation
- Coordinate systems in 2- and 3-dimensional geometries -
Cartesian, plane-polar, cylindrical and spherical polar
coordinate systems
- Two-dimensional and three-dimensional integrals and their application
to finding volumes and masses
-
Series Expansions, Limits and Convergence
- Taylor and Maclaurin series, expansions of standard functions
- Curve Sketching
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:
-
Arfken G.B. and Weber H.J. (2001), Mathematical methods for physicists (5th edition), Academic Press, ISBN 0-120-59826-4 (UL: 510 ARF)
-
Spiegel M.R. (1971), Advanced Mathematics for Engineers and Scientists, Schaum Outline Series, McGraw-Hill, ISBN 0-070-60216-6 (UL: 510 SPI)
-
Stroud K.A. and Booth D.J. (2011), Advanced Engineering Mathematics (5th edition), Paulgrave, ISBN 978-0-23-027548-5 (UL: 510.2462 STR)
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 |
