Tensors and Fields (U01371)

? Credit Points : 10 ? SCQF Level : 10 ? Acronym : PHY-3-TensFlds

This course provides an introduction to tensors and their uses in physics. Topics covered include: vectors, bases, determinants and the index notation; the general theory of Cartesian tensors; rotation and reflection tensors; various applications including elasticity theory - stress and strain tensors; orthogonal curvilinear coordinates, grad, div and curl; the divergence and Stokes' theorem, Laplacians; delta functions; applications to electromagnetism: scalar potential theory, e.g. Gauss's Law, dipoles, multipole expansions, solutions of Laplace's & Poisson's equations.

Entry Requirements

? Pre-requisites : Foundations of Mathematical Physics (PHY-2-FoMP) or Principles of Mathematical Physics (PHY-2-PoMP) and Methods of Applied Mathematics (MAT-2-MAM). Students intending on taking Tensors & Fields in Junior Honours must have obtained a minimum grade of 'C' in Foundations of Mathematical Physics (PHY-2-FoMP) or a minimum average grade of 'C' in Principles of Mathematical Physics (PHY-2-PoMP) and Methods of Applied Mathematics (MAT-2-MAM).

? Co-requisites : Lagrangian Dynamics(PHY-3-LagDyn), Mathematical Physics 3 (PHY-3-MathPhys3). Students wishing to take both Lagrangian Dynamics and Tensors & Fields should enrol for Mathematical Physics 3 (PHY-3-MathPhys3).

? Prohibited combinations : U01370 Lagrangian Dynamics

Subject Areas

Home subject area

Undergraduate (School of Physics), (School of Physics, Schedule Q)

Delivery Information

? Normal year taken : 3rd year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 3 hour(s) per week for 11 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Tuesday	11:10	12:00	KB
Lecture	Friday	11:10	12:00	KB

? Additional Class Information : Workshop/tutorial sessions, as arranged.

Summary of Intended Learning Outcomes

Upon successful completion of this course it is intended that a student will be able to:
1)be confident with the index notation and the Einstein summation convention
2)have a good working knowledge of matrices and determinants and be able to derive vector identities
3)understand the meaning and significance of tensors and their application to simple physical situations
4)understand and manipulate various orthogonal curvilinear co-ordinates
5)be familiar with the divergence and Stokes' theorem
6)appreciate the Dirac delta function
7)understand the meaning of a field and potential
8)apply the methods of solution of potential theory to various situations (mainly electrostatic)
9)to be able to apply what has been learnt in the course to solving new problems