MP2A: Vectors, Tensors and Fields (U03869)

? Credit Points : 10 ? SCQF Level : 8 ? Acronym : PHY-2-MP2A

Provides an introduction to Mathematical Physics and training in the associated concepts and calculational skills. Essential mathematical techniques are developed and deployed to construct physical theories and derive solutions to physical problems, thus integrating Mathematics and Physics. The content includes vectors and bases; tensors, eigenvectors and physical applications; scalar and vector fields; vector calculus and applications; potential theory.

Entry Requirements

? Pre-requisites : Physics 1A: Foundations (PHY-1-A) or SCE Advanced Higher or A Level Physics and Mathematics at A Grade; specialist courses in Mathematics (Year 2): Foundations of Calculus, Several Variable Calculus or suitable performance in AM3 (MAT-2-am3) and MM3 (MAT-2-mm3)

? Prohibited combinations : Foundations of Mathematical Physics (PHY-2-FoMP); AM4 (MAT-2-am4) and MM4 (MAT-2-mm4).

Subject Areas

Home subject area

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

Delivery Information

? Normal year taken : 2nd year

? Delivery Period : Semester 2 (Blocks 3-4)

? Contact Teaching Time : 4 hour(s) per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
13/01/2009	11:00	12:00	Lecture Theatre C, JCMB	KB

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 : Workshops two hours per week, as arranged.

Summary of Intended Learning Outcomes

1)understand vector spaces,linear independence,dimensionality,basis vectors, vector products and their physical significance
2)fluency in suffix notation,summation convention,Kronecker delta,Levi-Civita symbols
3)state transformation properties of scalars, vectors & tensors under change of basis
4)define Cartesian tensors of arbitrary rank; and give physical examples, such as the projection tensor
5)compute inertia tensor of systems of point masses,solid bodies
6)understand eigenvalues,eigenvectors;compute principal moments of inertia & axes
7)diagonalise symmetric 2nd-rank tensors;understand degeneracy & relation to symmetry
8)understand vector & scalar fields,level surfaces,flow lines
9)define gradient,directional derivative,div,curl,Laplacian
10)derive and use vector operator identities
11)define and compute line,surface and volume integrals; state and use the divergence and Stokes' theorems