PX1222: Mathematical Methods for Physicists 2
| School | Cardiff School of Physics & Astronomy |
| Department Code | PHYSX |
| Module Code | PX1222 |
| External Subject Code | 100425 |
| Number of Credits | 10 |
| Level | L4 |
| Language of Delivery | English |
| Module Leader | Dr Bernard Richardson |
| Semester | Spring Semester |
| Academic Year | 2015/6 |
Outline Description of 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.
On completion of the module a student should 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.
How the module will be delivered
Lectures 22 x 1 hr, weekly Exercise classes, marked exercises.
Skills that will be practised and developed
Problem solving. Investigative skills. Mathematics. Analytical skills.
How the module will be assessed
Examination and Continuous Assessment
Assessment Breakdown
| Type | % | Title | Duration(hrs) |
|---|---|---|---|
| Exam - Spring Semester | 60 | Mathematical Methods For Physicists Ii | 2 |
| Written Assessment | 40 | Mathematical Methods For Physicists Ii | N/A |
Syllabus content
Argand diagrams. Polar & Euler representations. De Moivre’s theorem. Complex functions. Physical applications of complex numbers. Relationship to 2D vectors and matrices.
Differentiation of a vector. Gradient vector. Conservative and non-conservative fields. Examples from physics. Differentiation of a function of more than one variable.
Partial differentiation. Idea of div, grad and curl (briefly). Stationary values, maxima and minima. Conditional stationary values.
Ordinary Differential equations in physics. Setting up physical problems. General Classification of ODEs. Superposition theorems. Boundary conditions
Second-order linear homogeneous equations. Examples
Second-order linear inhomogeneous equations. Particular integrals and complementary functions. Trial solutions. Simple harmonic examples.
Introduction to Fourier series.
Partial Differential Equations in physics. Examples (brief): Wave equation, heat equation, diffusion, Schrodinger equation.
Separation of variables method of solving PDE.
Probability Axioms. Discrete Events. Probability Distributions. Binomial and Poisson distributions.
Normal distribution, Random walks and diffusion. Means and variances. Relevance to statistical treatment of errors.
Background Reading and Resource List
Foundation Mathematics for the Physical Sciences, K F Riley and M P Hobson (CUP).