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DRPS : Course Catalogue : School of Physics and Astronomy : Undergraduate (School of Physics and Astronomy)

Undergraduate Course: Methods of Theoretical Physics (PHYS10105)

Course Outline
SchoolSchool of Physics and Astronomy CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits20 ECTS Credits10
Summary
One half of the course, Complex Calculus, provides an introduction to complex numbers and analytic functions. We discuss the general properties of such functions, and develop the machinery of their differential and integral calculus. A special emphasis is placed on using the Residue Theorem to evaluate real integrals. We introduce the Fourier and Laplace transforms and demonstrate how they can be used in solving linear PDEs.

The other half of the course, Vectors, Tensors, and Continuum Mechanics, provides an introduction to Cartesian tensors, rotation and reflection symmetries, and the basics of the underlying group structures. These concepts are then applied to continuum mechanics, using tensor arguments to formulate and explore ¿linear elasticity¿, the theory of elastic bodies and their deformations, in terms of strain and stress tensors.
Course description Vectors, Tensors, and Continuum Mechanics.
* Vectors, bases, Einstein summation convention, delta and epsilon symbols, matrices, determinants.
* Change of basis
- Invariance of physical laws: rotation of bases/change of frame
- composition of rotations, reflections, projections
- passive vs. active transformations
* The SO(3) symmetry group
* Cartesian tensors:
- definition/transformation properties and rank
- quotient theorem, pseudotensors, delta and epsilon as tensors
- isotropic (pseudo)tensors
- applications of tensor methods: simplifying integrals
* Taylor's theorem: the one- and three-dimensional cases
* Linear Elasticity
- deformations and examples including stretches and shears
- the strain tensor, stretching and shear
- the stress tensor, and some properties
- generalised Hooke's Law, isotropic media
- bulk and shear modulus and related constants
- examples in curvilinear coordinates
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Dynamics and Vector Calculus (PHYS08043) AND Fourier Analysis and Statistics (PHYS09055) OR Fourier Analysis (PHYS09054)
Co-requisites
Prohibited Combinations Students MUST NOT also be taking Electromagnetism and Relativity (PHYS10093) AND Honours Complex Variables (MATH10067)
Other requirements None
Information for Visiting Students
Pre-requisitesNone
High Demand Course? Yes
Course Delivery Information
Academic year 2024/25, Available to all students (SV1) Quota:  50
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 6, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 106 )
Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment) Coursework: 20%
Examination: 80%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)3:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. State in precise terms the foundational principles of complex analysis and linear elasticity and how they relate to broader physical principles.
  2. Devise and implement a systematic strategy for solving a complex problem in complex analysis or linear elasticity by breaking it down into its constituent parts.
  3. Apply a wide range of mathematical techniques, such as Cauchy's Integral Formula, Residue Theorem, Fourier and Laplace transforms, solving ODEs and PDEs, asymptotic matching technique, etc., to build up the solution to a complex problem in theoretical physics.
  4. Use experience and intuition gained from solving physics problems to predict the likely range of reasonable solutions to an unseen problem.
  5. Resolve conceptual and technical difficulties by locating and integrating relevant information from a diverse range of sources.
Reading List
None
Additional Information
Graduate Attributes and Skills Not entered
KeywordsMoTP
Contacts
Course organiserDr Miguel Martinez-Canales
Tel: (0131 6)51 7742
Email: miguel.martinez@ed.ac.uk
Course secretaryMs Nicole Ross
Tel:
Email: nicole.ross@ed.ac.uk
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