PX1121 MECHANICS AND MATTER - Cardiff School of Physics and ...

PX1222 MATHEMATICAL METHODS FOR PHYSICISTS II
MODULE INFORMATION:
Spring semester: 10 credits.
Module organiser: Dr E Pascale.
Deputy Module Organiser: Prof B S Sathyaprakash.
Teaching and feedback methods: Lectures 22 x 1 hr, weekly exercise classes, marked exercises.
Assessment: Examination 60%. Coursework 40%. [Examination duration: 2 hours]
Pre-cursors: PX1122 (excepting joint Maths/Physics students).
Co-requisites: None.
Pre-requisites: None.
AIMS OF THE MODULE:
To provide the basic theoretical techniques required during first-year physics courses.
To give post-A-Level students a solid grounding in complex numbers, vector calculus, second-order differential equations,
matrices and basic probability theory.
To give students practice in applying mathematical techniques to abstract and physical problems.
LEARNING OUTCOMES:
The student will be able to:
Demonstrate proficiency at basic representations, operations and applications of complex numbers.
Demonstrate an understanding of the meaning of scalar and vector fields, and demonstrate the application of grad, div,
curl, Laplacian to the formulation of the laws of physics.
Set up and solve simple first-order differential equations.
Show proficiency in using techniques for solving first- and second-order differential equations.
Show familiarity with basic probability distributions, statistical measures and their use.
OUTLINE SYLLABUS:
1. Argand diagrams. Polar and Euler representations. De Moivre’s theorem. Complex functions. Physical applications of
complex numbers. Relationship to 2D vectors and matrices.
2. Differentiation of a vector. Gradient vector. Conservative and non-conservative fields. Examples from physics.
Differentiation of a function of more than one variable.
3. Partial differentiation. Idea of div, grad and curl (briefly). Stationary values, maxima and minima. Conditional stationary
values.
4. Ordinary differential equations in physics. Setting up physical problems. General classification of ODEs. Superposition
theorems. Boundary conditions
5. Second-order linear homogeneous equations. Examples.
6. Second-order linear inhomogeneous equations. Particular integrals and complementary functions. Trial solutions. Simple
harmonic examples, use of .
7. Introduction to Fourier series.
8. Partial differential equations in physics. Examples (brief): Wave equation, heat equation, diffusion, Schrodinger equation.
9. Separation of variables method of solving PDE.
10. Probability Axioms. Discrete Events. Probability Distributions. Binomial and Poisson distributions.
11. Normal distribution, random walks and diffusion. Means and variances. Relevance to statistical treatment of errors.
TRANSFERABLE SKILLS:
Problem solving. Investigative skills. Mathematics. Analytical skills.
READING LIST:
Modern Engineering Mathematics, G James (Addison Wesley).
Mathematical Methods for Physics and Engineering, K F Riley, M P Hobson and S J Bence (Cambridge University Press).