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Unit information: Essential Maths for Physics in 2019/20

Please note: It is possible that the information shown for future academic years may change due to developments in the relevant academic field. Optional unit availability varies depending on both staffing and student choice.

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 Dr. Hanna
Open unit status Not open
Pre-requisites

None.

Co-requisites

MATH11004, PHYS10006, PHYS10005

School/department School of Physics
Faculty Faculty of Science

Description

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 details

The unit is taught though 12 two hour lectures. Each lecture includes both formal teaching and practice at problem solving assisted by post-graduate teaching assistants.

Weekly tutorials in groups are provided to assist students with the weekly set problem sheets.

Assessment Details

Weekly problems are both formative (through discussion in tutorials and written feedback) and summative to encourage students to take them seriously 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 unseen examination (80%).

Reading and References

  • Jordan and Smith, Mathematical Techniques
  • Boas, Mathematical Methods in the Physical Sciences.

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