Unit information: Maths with Numerical Modelling for Physics in 2023/24

Unit name Maths with Numerical Modelling for Physics PHYS10008 20 C/4 Teaching Block 2 (weeks 13 - 24) Professor. Annett Not open Normally A-level Physics and A-level Mathematics or equivalent. PHYS10006 Core Physics I, PHYS10005 Core Physics II, PHYS11400 School of Physics Faculty of Science

Unit Information

This unit will provide practice and training in the mathematics needed to complete the first year Physics courses and lay the foundations for subsequent years.

Topics covered include:

• The equation of heat conduction, and its solution by half-range Fourier series
• Partial differentiation, the gradient vector and its physical meaning
• Contours; tangents and normals to curves
• Change of variables and the chain rule
• Maxima and minima; stability of equilibrium
• Parametric curves, line integrals and work done by a force; conservative fields
• Exact differentials
• Double integrals, including change of variables and polar coordinates; application to moments of inertia
• Green's Theorem relating line integrals to double integrals; application to magnetic field generated by a current
• Matrix algebra, matrices as transformations of vectors, rotation and reflection matrices
• Determinants. Inverse matrix. Eigenvalues of 2 x 2 and 3 x 3 matrices, and application to vibrations.

Further, the course will introduce basic computer programming in Python to permit students to explore the mathematical concepts above through:

• evaluation of functions and series
• plotting functions and data in 2-D and 3-D
• simple matrix algebra solutions to sets of linear equations.

Aims:

• To motivate students to learn mathematics, by showing it in action in physics
• to develop students' mathematical skill and introduce the mathematical tools needed for first-year Physics
• to introduce basic programming skills useful for illustrating mathematical and physical principles, which will be built upon in computing courses in later years.

After completing this unit students should:

• be able to solve problems using partial differentiation, line integrals, double integrals, Fourier series, matrix algebra, and calculation of eigenvalues and eigenvectors of simple 2 x 2 and 3 x 3 matrices
• have an appreciation of the physical meaning and application of: the gradient vector, line integrals and conservative fields, Fourier series, and eigenvalues
• be able to write and test basic scientific programs using Python
• be able to visualise simple mathematical functions by generating plots in 2-D and 3-D
• be able to demonstrate principles of linear algebra using numerical libraries in Python.

How you will learn

The unit will be taught through a combination of

• asynchronous online materials, including narrated presentations and worked examples
• synchronous group problems classes, workshops, tutorials and/or office hours
• asynchronous directed individual formative exercises and other exercises

How you will be assessed

Weekly mathematics problems are both formative (through discussion in tutorials and written feedback) and summative.

The computing will be assessed formatively through regular online assessment of individual and pair-based work. The computing coursework and final extended exercise will be assessed summatively.

The final assessment mark for the unit is made up of:

• Mathematics weekly set written/e-assessment problems (10%)
• Computing coursework (30%)
• Mathematics examination (40%)
• Computing extended exercise (20%).

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. PHYS10008).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.