# PX161 Tutorial (Physics)

##### Coordinator: Michael Pounds

##### Weighting: 10 CATS

This is a composite module made of 2 components: physics problems (5 credits) and five worksheets (5 credits). Problem solving forms a vital part of the learning process and therefore each lecturer issues a set of problems for their module which you are expected to make serious attempts to solve. A subset of these problems is marked for credit. These problems are discussed in the weekly Examples Classes.

**Aims:**

To cover background mathematical material assumed by other modules, to give experience of learning by self-study and to develop the habit of keeping up with the problem sheets handed out in physics modules

**Objectives:
**

By the end of the module, students should be able to:

- Demonstrate a facility with complex numbers, curve sketching, the mathematics used to model waves, integration and Fourier methods
- Tackle problems associated with the physics covered by year 1 modules

**Syllabus:**

**Techniques**

Revision of mathematics from A-level - mainly algebra, differentiation, integration and trigonometry

**Worksheets**

**Complex Numbers**Their construction from the reals; norm, argument, real and imaginary parts; addition, subtraction, multiplication and division; the Argand diagram and geometric view of complex numbers. de Moivre's theorem, exponential representation of a complex number in terms of its norm and its argument.

**Curve Sketching**Basic Functions: trigonometric, exponential, modulus. Odd/even functions. Limiting values, continuity, differentiability. L'Hopital's rule. Asymptotes and strategies for graph sketching.

**Maths for Waves**Notation for partial derivatives. Examples of equations admitting wave-like solutions: wave equation, advection equation, traffic flow. Linear operators, principle of superposition. Boundary conditions, reflection and transmission coefficients. Plane waves, exponential form. Energy in waves. Wave groups, group velocity.

**Integration along Lines, Surfaces and Volumes**Notation for integration of both scalar and vector quantities over lines, surfaces and volumes. Integration along lines using parameterised curves, circulation around a contour. Infinitesimal surface element as a vector in 3D, use to compute flux across a surface. Volume integrals and revision of the Jacobian.

**Fourier Series**Revision of lectured material: definition of Fourier series, the coefficients, periodic extensions, Gibbs phenomenon. The complex form, Parseval's theorem. Functions on intervals of length 2L. Introduction to Fourier transforms as the limit of L -> infinity.

You should answer the questions on each of the worksheets and hand in your answers to your personal tutors as directed.

**Weekly Problem Sheets**

You will be asked to hand in written answers to designated problems from the problem sheets or attempt designated problems from the Mastering Physics package.

**Operation**

**Mathematics**

All students will take a diagnostic mathematics test in the 1st week of the year. This test has 4 sections - algebra, trigonometry, differentiation and integration. Students failing any section will be required to be retested in that section (a total of 2 retests will be available and the best mark obtained will count). Students failing a section will be given work sheets and there will be surgeries where students can obtain individual assistance.

**Mathematics Worksheets**

Students will receive copies of each worksheet. These are self-study with problems which should be attempted and submitted to personal tutors for marking.

**Physics Problems**

For each physics module a number of problems will be set and a number of these will be identified as 'for credit'. Following submission of their attempts at these problems each student will attend a weekly small group seminar in which solutions to the problems will be presented by a tutor. Some of the assessments will be paper based and others will be web based.

**Assessment:** Worksheets - 50%; Physics Problems - 50%.