Foundations of Mathematical Physics (U00547)

? Credit Points : 20 ? SCQF Level : 8 ? Acronym : PHY-2-FoMP

Provides an introduction to Mathematical Physics for all single-honours Physics students. Essential mathematical techniques are developed and deployed in the context of physical problems, thus consolidating and integrating Mathematics and Physics. The content includes ordinary differential equations and particle dynamics, central forces, coupled oscillators, vectors and bases, tensors and eigenvectors, scalar and vector fields, vector calculus, potential theory.

Entry Requirements

? Pre-requisites : Physics 1A: Foundations (PHY-1-A); AM3 (MAT-2-am3) and MM3 (MAT-2-mm3) or specialist courses in Mathematics (Year 2).

? Prohibited combinations : Principles of Mathematical Physics (PHY-2-PoMP); Methods of Applied Mathematics (MAT-2-MAM); AM4 (MAT-2-am4) and MM4 (MAT-2-mm4).

Subject Areas

Home subject area

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

Delivery Information

? Normal year taken : 2nd year

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

? Contact Teaching Time : 5 hour(s) per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
08/01/2007	11:10	12:00	Lecture Theatre C, JCMB	KB

All of the following classes

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

? Additional Class Information : Workshops three hours per week, as arranged.

Summary of Intended Learning Outcomes

1)understand vectors and use for physical quantities;define scalar,vector products;vector equns for points,lines,planes
2)understand vector spaces,linear independence,dimensionality,basis vectors
3)use suffix notation,summation convention,Kronecker delta,Levi-Civita symbols
4)state transformation properties of vectors & scalars under change of basis
5)define Cartesian tensors of rank>1;give physical examples
6)compute inertia tensor of systems of point masses,solid bodies
7)understand eigenvalues,eigenvectors;compute principal moments of inertia & axes
8)diagonalise symmetric 2nd-rank tensors;understand degeneracy & relation to symmetry
9)understand vector & scalar field,level surfaces,flow lines
10)define gradient,directional derivative,div,curl,Laplacian;use vector operator identities,divergence & Stokes' theorems
11)define line,surface,volume integrals
12)Solve:linear 1st order differential equns(DEs) dy/dx=F(x,y); F separable or linear in y,graphically & numerically;linear 2nd order homogeneous and inhomogeneous DEs (constant coeffs)
13)Understand simple harmonic oscillator incl damping & sinusoidal driving forces;resonance.Classify solutions
14)Solve coupled linear DEs for >1 variable
15)Transform between e.g.Cartesian & polar coordinates
16)Set up dynamics DEs using Newton's 2nd Law
17)Linearise equns of motion
18)Formulate & solve DEs describing:motion with linear resistive forces in 1D & 2D;oscillatory systems incl simple & compound pendula;masses on springs
19)Set up & solve central force orbits;understand angular momentum & conservation
20)Understand:need for probability in physics;differences of frequentist & degree-of-belief definitions
21)Use assertions to formulate a problem;understand mutual independence,exclusivity,exhaustiveness
22)Understand and use Bayes' theorem,probability trees
23)Understand expectation values,moments
24)Understand binomial,Poisson,Gaussian distributions;central limit theorem,estimation of physical parameters,confidence limits