F19AB2 Applied mathematics B

(Third year module given in the second semester.)


Lecturer. Simon Malham, Room CM T.21, Mathematics Department.

Contact. email: S.J.A.Malham [at] hw.ac.uk and tel: 0131 451 3254.

Lectures. Monday 1:15pm in EM183, Thursday 9:15am in EM182 and Friday 11:15am in EM183.

Tutorials. Thursday at 3:15pm in CMB S01.

Vision. You can find all the lecture notes, handouts, solutions to exercises and past papers and so forth on the course VISION page.

Course aims and objectives. The objective of the module is to introduce some fundamental ideas and techniques in Applied Mathematics.


Assessment. The continuous assessment consists of a one hour midterm exam counting for 10 percent of the final mark, homework counting for 5 percent of the final mark (details below) and a two-hour final exam at the end of term which counts for 85 percent of the course mark. The midterm will be held on

Thursday February 18th

The homework assessment consists of the specified exercises in the table below, to be handed in before or on the dates indicated. You can score up to 20 marks per homework. Your best 5 homeworks out of the 7 will be added together to generate your overall continuous assessment score (for maximum credit you need to score a total of 100 marks).

There is a resit in August for the ordinary course. The resit assessment is purely on the basis of a two-hour exam.

Contract. Students are expected to read the notes before, during and after the lectures and tutorials. Lectures will act as a more formal forum for the lecturer to explain the ideas of the course and give alternative examples, whilst tutorials will take a less formal and more personal form. There are exercises at the end of each chapter and students must attempt these. Mathematics is best learned through grappling with the underlying ideas presented in lectures and then tackling problems given in the exercises.

You cannot learn to swim by reading a book about it!

Hence try the exercises, and if you get stuck, ask the lecturer either after a lecture, during the tutorials. It is vital that you can solve problems proficiently. If you need help, then

Ask, ask, ask!

Attendance sheets. Students will be required to sign an attendance sheet with their initials in every lecture and tutorial. If any one student misses three consecutive such contact events, or more than one-third of them overall up until that date, then their personal mentor will be contacted.

Evaluations. At the end the course students will have an opportunity to fill out formal university evaluations on the course.

Books. The two main recommended books are V.I. Arnold and Chorin and Marsden (see the bibliographies of the lecture notes for details).


Electronic resources

Syllabus (from the official department course pages)

Movies. These are the movies shown during the course. Download them and use them freely.

Brachistochrome: physical demonstration.
Brachistochrome: cycloid animation.
Soap bubble: catenoid demonstration.
Soap bubble: catenoid slow motion demonstration.
Fan Yang bubble show.
Hanging rope: Catenary curve.
Linear quadratic regulation: Inverted pendulum.
Linear quadratic regulation: Inverted pendulum robot.
Kepler problem movie 1.
Kepler problem movie 2.
Rattleback movie link.
Tippe top webpage link.
Tops, webpage link.
Taylor Couette flow experiment.
Chris Hadfield wringing a wet cloth on the ISS.
Water droplet movie
Bernoulli effect demonstration, Venturi tube.
Bernoulli effect demonstrations, other examples.
Torricelli Theorem educational video: Sarah Friedl.
Vortex shedding off a cylinder (experiment and numerical): Von Karmen vortex street.
Vortex shedding off a cylinder (numerical): Von Karmen vortex street.
Non-Newtonian fluid bath
Non-Newtonian fluid on speaker cone
Leapfrogging vortex rings
Colliding vortex rings
Toroidal flows
Low Reynolds number flow by G.I. Taylor
Vorticity (NSF)
Complete collection (21) of National Committee for Fluid Mechanics films (NSF) posted by Barry Belmont

Homework timetable

This may change slightly as we progress so keep checking this webpage.

There are 7 homeworks here, each is worth 20 marks. Your best 5 will be used to make your final score (which is worth 5% of your overall mark for the module).

Exercises Date due
Euler-Lagrange alternative form + Soap film Jan 29th
Hanging rope Feb 5th
Central force field Feb 12th
None---midterm this week. Feb 19th
1.4 Steady Oscillating Channel Flow and 1.5 Channel Shear Flow Feb 26th
Bernoulli Theorem execise to be handed out in class Mar 11th
Fourier series: question 1 Mar 18th
Heat equation: question 1 Mar 25th

This webpage and its content was started on 30/1/2009.

Please feel free to download and use any of the material accessible from this page---provided that it is not used for commercial gain.

Last updated: 18/2/2016.

S.J.A.Malham [at] hw.ac.uk