Undergraduate Course: Introductory Fields and Waves (PHYS08053)
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 |
None |
Taught in Gaelic? | No |
| Course description | It consists of two 10pt halves, running in parallel: Fields and Vector Calculus and Waves and Fourier Analysis, and provides a suitable preparation for core MP in JH, in particular Electromagnetism and Relativity, and Quantum Dynamics. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | No |
Course Delivery Information
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| Delivery period: 2014/15 Semester 2, Available to all students (SV1)
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Learn enabled: Yes |
Quota: None |
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Web Timetable |
Web Timetable |
| Course Start Date |
12/01/2015 |
| Breakdown of Learning and Teaching activities (Further Info) |
Total Hours:
200
(
Lecture Hours 44,
Supervised Practical/Workshop/Studio Hours 40,
Summative Assessment Hours 3,
Revision Session Hours 4,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
105 )
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| Additional Notes |
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| Breakdown of Assessment Methods (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
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| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S2 (April/May) | Introductory Fields and Waves | 3:00 | | | Resit Exam Diet (August) | Introductory Fields and Waves | 3:00 | |
Summary of Intended Learning Outcomes
- Develop a working knowledge of the elements of vector calculus, in differential and integral form, and the use of index notation and summation convention.
- Understand the application of vector calculus to the flow of ideal fluids, and problems in electrostatics and magnetostatics.
- Develop a working knowledge of the elements of Fourier Series and Fourier Transforms, and their application to a variety of linear systems.
- Understand a wide range of physical phenomena involving waves: reflection and refraction, dispersion, interference and diffraction, wave-particle duality.
- Devise and implement a systematic strategy for solving a simple problem by breaking it down into its constituent parts.
- Use the experience, intuition and mathematical tools learned from solving physics problems to solve a wider range of unseen problems.
- Resolve conceptual and technical difficulties by locating and integrating relevant information from a diverse range of sources. |
Assessment Information
| 80% exam 20% coursework |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Fields and Vector Calculus:
- Introduction: scalar and vector fields in gravitation and electrostatics. The need for vector calculus. Revision of vector algebra and products. Equations of line and planes. Solution of vector equations. [2]
- Index notation, Kronecker delta and epsilon symbols, summation convention. Application to vector algebra. [1]
- Equipotentials of a scalar field, gradient of a scalar field, interpretation, directional derivative. Del as an operator. Examples of calculating gradient, product rule and chain rule. Physical examples: Newton's law of gravitation, Coulomb's law, examples of scalar potentials. [2]
- Divergence, curl and the Laplacian. Geometrical interpretation. Vector operator identities: product rules, etc. Proofs using a mix of explicit Cartesians, index notation, and "quick tricks". Examples from electrostatics: linear superposition; electric dipole. [2]
- Curvilinear coordinates. Orthogonal curvilinear coordinates. Transforming coordinates between bases. Divergence, gradient, curl and the Laplacian in orthogonal curvilinears. [2]
- Revision of line integrals. Examples: work and energy, current loop. Surface integrals: definition and parametric form. Line and surface elements in curvilinear coordinates. Flux of a vector field through a surface. Example: fluid flow, electrostatics. Other surface integrals. Volume integrals over scalar and vector fields, parametric form and Jacobians. Examples: volume and centre of mass of solid bodies. [3]
- Integral definition of divergence; the divergence theorem (and Green's theorem). Corollaries of the divergence theorems. The continuity equation; sources and sinks (electrostatics and fluids). Conservation of mass and charge. Gauss's law for electrostatics: capacitors, images. [3]
- Line integral definition of curl; physical/geometrical interpretation; Stokes' theorem and its corollaries. Examples: Vorticity in ideal fluids. Currents, magnetic fields. [2]
- The scalar potential: path independence and scalar potential for conservative fields. Methods for finding scalar potentials. Conservative forces and energy conservation. More electrostatics and gravitation. Green's identities, Poisson and Laplace equations, methods of solution. [2]
- The vector potential: necessary conditions, uniqueness, construction of the vector potential. Examples from fluids and magnetostatics. Solenoids. Magnetic dipoles. [2]
Waves and Fourier Analysis:
- Elementary discussion: waves on a string, wave equation, elementary solutions, transverse vs longitudinal, wavelength, frequency, velocity, travelling and standing waves. [2]
- Stretched string from n-coupled oscillators. Linear superposition, standing waves, initial and boundary conditions, introduction to eigenfunction expansions. [2]
- Fourier Series: periodic functions, sine/cosine and full range series, complex series, Fourier's theorem, determining coefficients, solving ODEs with Fourier series. Parseval's theorem, convergence of Fourier Series. Square waves and Gibbs phenomenon. [3]
- Fourier Transforms: inversion formula, convolution theorem, Parseval¿s theorem, Fourier transforms of Gaussians. [3]
- Solution of ODEs with Fourier Transforms, e.g. forced damped harmonic oscillator. Expansion of general wave solution in modes, energy in waves, plane waves and spherical waves. [2]
- Linear response (and relation to convolution theorem), delta function, Greens functions for Poisson and Wave equation, causality. [2]
- Geometrical Optics: reflection and refraction at a plane boundary, lenses, dispersion, phase velocity and group velocity. [2]
- Huygens principle, interference, single and double- slit diffraction, diffraction gratings. [2]
- Photoelectric effect and double- slit diffraction revisited, De Broglie, wave- particle duality, Gaussian wave packets, Heisenberg uncertainty principle. [2] |
| Transferable skills |
Not entered |
| Reading list |
PC Matthews, Vector Calculus (Springer) - first choice for the maths bit
David J Griffths, Introduction to Electrodynamics (Prentice Hall) - first choice for the physics bits
DE Bourne and PC Kendall, Vector Analysis and Cartesian Tensors (Chapman and Hall)
KF Riley and MP Hobson, Essential Mathematical Methods for the Physical Sciences (CUP) ML Boas, Mathematical Methods in the Physical Sciences (Wiley)
GB Arfken and HJ Weber, Mathematical Methods for Physicists (Academic Press) MR Spiegel, Vector Analysis (Schaum); Fourier Analysis (Schaum)
TW Korner, Fourier Analysis (CUP)
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| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | IFW |
Contacts
| Course organiser | Dr Peter Boyle
Tel: (0131 6)50 5239
Email: paboyle@ph.ed.ac.uk |
Course secretary | Mrs Bonnie Macmillan
Tel: (0131 6)50 5905
Email: Bonnie.MacMillan@ed.ac.uk |
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