# Unit information: Essential Maths for Physics in 2023/24

Unit name Essential Maths for Physics PHYS11400 10 C/4 Teaching Block 2 (weeks 13 - 24) Professor. Annett Not open None. MATH11004, PHYS10006, PHYS10005 PHYS10008 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 2x2 and 3x3 matrices, and application to vibrations.

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.

## Your learning on this unit

Students will:

• be able to solve problems using partial differentiation, line integrals, double integrals, Fourier series, matrix algebra, and calculation of eigenvalues and eigenvectors of simple 2x2 and 3x3 matrices.
• have an appreciation of the physical meaning and application of: the gradient vector, line integrals and conservative fields, Fourier Series, and eigenvalues.

## 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 problems are both formative (through discussion in tutorials and written feedback) and summative. The final assessment mark for the unit is made up of:

• Weekly set written problems (10%)
• weekly set e-assessment problems (10%)
• final two hour examination (80%).

## 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. PHYS11400).

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.