PX1122: Mathematical Methods for Physicists 1
| School | Cardiff School of Physics & Astronomy |
| Department Code | PHYSX |
| Module Code | PX1122 |
| External Subject Code | 100403 |
| Number of Credits | 10 |
| Level | L4 |
| Language of Delivery | English |
| Module Leader | Dr Annabel Cartwright |
| Semester | Autumn Semester |
| Academic Year | 2015/6 |
Outline Description of Module
To provide the basic theoretical techniques required during first-year physics courses.
To introduce post-A-Level students to vectors, matrices, series, functions and graphs, and elementary calculus.
To give students practice in applying mathematical techniques to abstract and physical problems.
On completion of the module a student should be able to
Use vectors to describe positional coordinates and lines and relate them to Cartesian coordinates and show proficiency at basic vector operations and scalar and vector products and their applications. Application of vector algebra to solve simple problems in physics.
Demonstrate and understanding of how to perform and exploit basic matrix manipulations.
Show familiarity with and make use of series and expansions of trigonometric, exponential and logarithmic functions.
Show proficiency in plotting graphs of functions and their derivatives and at differentiation, partial differentiation and integration and their applications.
How the module will be delivered
Teaching and feedback methods: Lectures 22 x 1 hr, weekly Exercise classes, marked exercises.
Skills that will be practised and developed
Mathematics.
Problem solving.
Analytical skills.
How the module will be assessed
Examination and Continuous Assessment
Assessment Breakdown
| Type | % | Title | Duration(hrs) |
|---|---|---|---|
| Exam - Autumn Semester | 60 | Mathematical Methods For Physicists I | 2 |
| Written Assessment | 40 | Mathematical Methods For Physicists I | N/A |
Syllabus content
Vectors. Cartesian vectors. Importance in physics. Position. Force. Acceleration. Velocity, etc.
Operations on Vectors. Dot and cross product.. Angular momentum.
Physical interpretation and examples of vectors
Matrices. Definition and interpretation. Addition and Multiplication. Matrices operating on vectors, e.g. rotation in the plane.
Inverse of a matrix. Determinants. Use for solving simultaneous equations. Symmetric, antisymmetric and orthogonal matrices. Eigenvectors and eigenvalues for symmetric matrices.
Functions of a real variable. Exponential, trigonometric and hyperbolic functions. Physical examples. Series Expansions. Binomial and Taylor series. Approximations using truncated series.
Differentiation of powers, logarithms, exponential and trigonometric functions. Product, quotient and chain rules. Implicit and parametric differentiation.
Integration of powers, logarithms, exponential and trigonometric functions. Definite and indefinite integrals.
Area under a curve. Transforming variables. Integration by parts.
Line integrals, multiple integrals, volumes. Curvilinear coordinates, e.g. spherical polar coordinates, introduced through volume elements.
Solution of linear first-order ODEs by separation of variables and by integrating factor.
Background Reading and Resource List
Foundation Mathematics for the Physical Sciences, K F Riley and M P Hobson (CUP).