Undergraduate Course: Mathematics for Physics 4 (PHYS08038)
Course Outline
| School | School of Physics and Astronomy |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 8 (Year 2 Undergraduate) |
Credits | 20 |
| Home subject area | Undergraduate (School of Physics and Astronomy) |
Other subject area | None |
| Course website |
WebCT |
Taught in Gaelic? | No |
| Course description | This course is designed for pre-honours physics students, to learn the techniques of vector calculus, Fourier series and transforms, and simple partial differential equations to describe basic concepts in physics. The course consists of an equal balance between lectures to present new material, and workshops to develop understanding, familiarity and fluency. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | No |
Course Delivery Information
|
| Delivery period: 2011/12 Semester 2, Available to all students (SV1)
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WebCT enabled: Yes |
Quota: None |
| Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| King's Buildings | Lecture | | 1-11 | 11:10 - 12:00 | | | | | | King's Buildings | Lecture | | 1-11 | | 11:10 - 12:00 | | | | | King's Buildings | Lecture | | 1-11 | | | | 11:10 - 12:00 | | | King's Buildings | Lecture | | 1-11 | | | | | 11:10 - 12:00 | | King's Buildings | Tutorial | Waves Workshop | 2-11 | 14:00 - 15:50 | | | or 14:00 - 15:50 | | | King's Buildings | Tutorial | Fields Workshop | 2-11 | | 14:00 - 15:50 | | | or 14:00 - 15:50 |
| First Class |
Week 1, Monday, 11:10 - 12:00, Zone: King's Buildings. JCMB Lecture Theatre B (Waves lecture) |
| Exam Information |
| Exam Diet |
Paper Name |
Hours:Minutes |
|
|
| Main Exam Diet S2 (April/May) | | 3:00 | | | | Resit Exam Diet (August) | | 3:00 | | |
Summary of Intended Learning Outcomes
On completion of this course it is intended that student will be able to
&· Demonstrate understanding and work with vector fields and the basic operations of vector calculus, and apply these to a range of problems from of heat flow, fluid flow, electrostatics, and potential theory.
&· Demonstrate understanding and work with line, surface and volume integrals, and the associated theorems of Green, Stokes and Gauss, and to apply these to physical problems, for example, fluid flow, heat flow and electromagnetism.
&· Demonstrate understanding and work with Fourier series and complex functions, their applications to the solution of ordinary differential equations and elementary physical examples such as standing waves.
&· Demonstrate understanding of the Fourier Transform, inversion formula, convolution and Parseval's theorem. To apply these to a range of physical situations, for example, harmonic oscillators and travelling waves, and understand the link to the uncertainty principle.
&· Demonstrate understanding of the use of linear response functions, their relation to convolution and associated delta and Green's functions, and to apply these to inhomogenous static and dynamical problems (Poisson and sources of waves).
|
Assessment Information
20% coursework
80% examination |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Fields
1. vector fields, grad, div and curl, the Laplacian, identities, potential theorems, polar coordinates, Laplace and Poisson equations, boundary value problems, with examples from fluid flow, heat flow, electrostatics;
2. Line, surface and volume integrals, and evaluation thereof in rectangular and polar co-ordinates, integral theorems (Green, Gauss & Stokes), conservation laws (mass in fluids, charge in electromagnetism, circulation around closed curves in fluids).
Waves
1. Fourier Series: complex fns, Fouriers Thm, determining coefficients, solving ODEs with Fourier series, linear algebra view, simple physics examples in terms of standing waves, bound states;
2. Fourier Transform: inversion formula, convolution, Parseval, uncertainty principle, forced damped harmonic oscillator, expansion of solutions, travelling waves;
3. Linear response (and reln to convolution thm), delta function and Greens functions (Poisson and Waves). |
| Transferable skills |
Not entered |
| Reading list |
Not entered |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | MfP4 |
Contacts
| Course organiser | Dr Brian Pendleton
Tel: (0131 6)50 5241
Email: b.pendleton@ed.ac.uk |
Course secretary | Miss Leanne O'Donnell
Tel: (0131 6)50 7218
Email: l.o'donnell@ed.ac.uk |
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© Copyright 2011 The University of Edinburgh - 16 January 2012 6:40 am
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