Undergraduate Course: Introductory Fields and Waves (PHYS08053)
Course Outline
| School | School of Physics and Astronomy |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 8 (Year 2 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 20 |
ECTS Credits | 10 |
| Summary | 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. |
| Course description |
Fields and Vector Calculus:
Vectors:
- Revision of vector algebra and products. Equations of line and planes. Solution of vector equations. [2]
- Suffix notation, Kronecker delta and epsilon symbols, summation convention. Application to vector algebra. [3]
- Orthonormal bases, change of bases and Transformation laws for scalars, vectors and pseudovectors [2]
Fields and Vector Calculus:
- Scalar and vector fields in gravitation and electrostatics. The need for vector calculus [1]
- Equipotentials of a scalar field, gradient of a scalar field, interpretation, directional derivative [1]
- Del as an operator. Examples of calculating gradient, product rule and chain rule. [1]
- 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". [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. [2]
Electrostatics and Potential Theory:
- Electric Force and Electric Field, point charges and Dirac delta function. Coulomb's law and potential due to point charge [2]
- Integral definition of divergence; the divergence theorem. Corollaries of the divergence theorems. The continuity equation; sources and sinks in electrostatics. Conservation of mass and charge. Gauss's law for electrostatics; solving problems using symmetry. [3]
- Line integral definition of curl; physical/geometrical interpretation; Stokes' theorem and its corollaries. [1]
- The scalar potential: path independence and scalar potential for conservative fields. Methods for finding scalar potentials. Conservative forces and energy conservation. [1]
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]
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Information for Visiting Students
| Pre-requisites | None |
Course Delivery Information
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| Academic year 2015/16, Available to all students (SV1)
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Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| 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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| Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
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| Additional Information (Assessment) |
80% exam 20% coursework |
| Feedback |
Not entered |
| 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 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Mastery of suffix notation and summation convention and its use in relation to vectors and orthonormal bases. Knowledge of change of basis, orthogonal matrices and transformation laws for vectors and pseudovectors transformation
- A thorough knowledge of the elements of vector calculus, in differential and integral form. Understanding of the physical significance of div, grad and curl; a thorough knowledge of the application of vector calculus to the theory of electrostatics and associated calculational problems.
- 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.
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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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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | IFW |
Contacts
| Course organiser | Prof Peter Boyle
Tel: (0131 6)50 6573
Email: |
Course secretary | Mrs Bonnie Macmillan
Tel: (0131 6)50 5905
Email: |
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