Undergraduate Course: Physical Mathematics (PHYS09015)

Course Outline
School	School of Physics and Astronomy	College	College of Science and Engineering
Course type	Standard	Availability	Available to all students
Credit level (Normal year taken)	SCQF Level 9 (Year 3 Undergraduate)	Credits	10
Home subject area	Undergraduate (School of Physics and Astronomy)	Other subject area	None
Course website	http://www2.ph.ed.ac.uk/~paboyle/Site/Physical_Mathematics.html	Taught in Gaelic?	No
Course description	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 (not applicable to Visiting Students)
Pre-requisites	Students MUST have passed: Foundations of Mathematical Physics (PHYS08024) OR ( Applicable Mathematics 4 (Phys Sci) (MATH08017) AND Mathematical Methods 4 (Phys Sci) (MATH08018)) OR ( MP2A: Vectors, Tensors and Fields (PHYS08032) AND MP2B: Dynamics (PHYS08033)) Students MUST have passed: Physics 2A (PHYS08022) AND Physics 2B (PHYS08023)	Co-requisites
Prohibited Combinations		Other requirements	None
Additional Costs	None

Information for Visiting Students
Pre-requisites	None
Displayed in Visiting Students Prospectus?	Yes

Course Delivery Information

Delivery period: 2012/13 Semester 1, Available to all students (SV1)						WebCT enabled: Yes		Quota: None
Location	Activity	Description	Weeks	Monday	Tuesday	Wednesday	Thursday	Friday
King's Buildings	Lecture		1-11		10:00 - 10:50
King's Buildings	Lecture		1-11					10:00 - 10:50
King's Buildings	Tutorial		2-11		11:10 - 13:00 or 14:00 - 15:50
First Class	First class information not currently available
Additional information	Workshop/tutorial sessions, as arranged.
Exam Information
Exam Diet	Paper Name		Hours:Minutes
Main Exam Diet S2 (April/May)			2:00
Resit Exam Diet (August)			2:00

Delivery period: 2012/13 Semester 1, Part-year visiting students only (VV1)						WebCT enabled: No		Quota: None
Location	Activity	Description	Weeks	Monday	Tuesday	Wednesday	Thursday	Friday
King's Buildings	Lecture		1-11		10:00 - 10:50
King's Buildings	Lecture		1-11					10:00 - 10:50
King's Buildings	Tutorial		2-11		11:10 - 13:00 or 14:00 - 15:50
First Class	First class information not currently available
Additional information	Workshop/tutorial sessions, as arranged.
Exam Information
Exam Diet	Paper Name		Hours:Minutes
Main Exam Diet S1 (December)			2:00

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

Assessment Information
Degree Examination, 100% Visiting Student Variant Assessment Degree Examination, 100%

Special Arrangements
None