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Essential Maths for Physics
Unit information: Essential Maths for Physics in 2020/21
Please note: you are viewing unit and programme information
for a past academic year. Please see the current academic year for up to date information.
Unit name |
Essential Maths for Physics |
Unit code |
PHYS11400 |
Credit points |
10 |
Level of study |
C/4
|
Teaching block(s) |
Teaching Block 2 (weeks 13 - 24)
|
Unit director |
Professor. Annett |
Open unit status |
Not open |
Pre-requisites |
None.
|
Co-requisites |
MATH11004, PHYS10006, PHYS10005
|
School/department |
School of Physics |
Faculty |
Faculty of Science |
Description including Unit Aims
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.
Intended Learning Outcomes
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.
Teaching Information
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
- guided, structured reading
Assessment Information
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%).
Reading and References
- Jordan and Smith, Mathematical Techniques
- Boas, Mathematical Methods in the Physical Sciences.