Physical Mathematics (U01353)

? Credit Points : 10 ? SCQF Level : 9 ? Acronym : PHY-3-PhMath

An introduction to mathematical ideas and techniques for other courses in Honours years. The key idea is that of complete sets of orthonormal vectors, and its generalisation to complete sets of orthonormal functions. These functions occur in the solution (by separation of variables) of frequently-encountered partial differential equations in physics, such as Poisson's equation (in electrostatics), the wave equation and the Schrodinger equation. Some of the material will have been covered before in second-year courses; this material will be reviewed and developed, the emphasis throughout being on gaining physical insight into the mathematics.

Entry Requirements

? Pre-requisites : Physics 2A: Forces, Fields and Potentials (PHY-2-A); Foundations of Mathematical Physics (PHY-2-FoMP) or Applicable Mathematics 4 and Mathematical Methods 4 (MAT-2-am4/mm4) or Principles of Mathematical Physics (PHY-2-PoMP).

? Prohibited combinations : Complex Variable & Differential Equations (MAT-3-CVD).

Variants

? This course has variants for part year visiting students, as follows

Physical Mathematics (VS1) (Semester 1 (Blocks 1-2))

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

First Class Information

Date	Start	End	Room	Area	Additional Information
19/09/2006	11:00	12:00	Lecture Theatre B, 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 : Workshop/tutorial sessions, as arranged.

Summary of Intended Learning Outcomes

Upon satisfactory completion of the course, students should be able to:
1)Relate complete sets of orthonormal vectors and complete sets of orthogonal functions
2)Sketch elementray functions such as the gaussian, the sinc, the ln, and trigonometric functions
3)State the fundamental equations of Sturm-Liouville theory and its applications to physical problems. Solve some simple Sturm-Liouville problems
4)Write down some common partial differential equations in physics, i.e. the diffusion equation, the wave equation and Poisson's equation; identify and use the coordinate system best suited to the symmetry of the problem to solve these partial differential equations in simple cases
4)Write down the expressions for the expansion of a function in a Fourier series and its generalisation to Fourier transforms; calculate Fourier series and Fourier transforms of simple functions
5)Use Fourier series and Fourier transforms to solve the diffusion and wave equations
6)Describe the concept of a Green's function
7)Acquire a degree of familiarity with the MAPLE mathematical software environment