F19AB2 Applied mathematics B

(Third year module given in the second semester.)


Introduction

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

Contact. email: simonm@ma.hw.ac.uk and tel: 0131 451 3254.

Lectures. Monday 2:15pm in SR320, Tuesday 10:15am in SR320 and Friday 9:15am in SR320.

Tutorials. One a week: Friday at 10:15am in SR320.

Webpages. This course homepage where you can download lecture notes, further handouts, solutions to the exercises, past papers is:

http://www.ma.hw.ac.uk/~simonm/F19AB2/

More information about the module can be found at:

http://www.ma.hw.ac.uk/maths/modules/F19AB2

which can also be reached from the Mathematics Department's Homepage --> Teaching --> Information for students already on course --> Modules mainly taken by Mathematics and AMS students.

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

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

Syllabus.

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

Tuesday 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.

Calculators. In the final exam you will only be allowed to use either the Casio fx-85WA or fx-85MS. This is a University regulation. Personally, I do not think you will need a calculator.

Contract. Students are expected to read the notes in this booklet 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).


Announcements


Electronic resources


PDF files are recommended for printing. denotes files not yet available.

Syllabus (from the official department module pages)

Lecture notes.

An introduction to Lagrangian and Hamiltonian mechanics
Introductory fluid mechanics
Fourier series (by Ken Brown and Robert Weston)
Heat equation (Separation of variables, by Ken Brown and Robert Weston)
Laplace equation (Separation of variables, by Ken Brown and Robert Weston)
Wave equation (Separation of variables, by Ken Brown and Robert Weston)

Exercises and solutions. The solutions will be made available as the course progresses.

Topic/Exercise sheet Date out Solutions
An introduction to Lagrangian and Hamiltonian mechanics Beg Feb Solutions
Introductory ideal fluid mechanics Beg Mar Solutions
PDEs/Separation of variables Mid Mar Solutions

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

Rattleback movie link
Water droplet movie link
Non-Newtonian fluid bath movie link
Leapfrogging vortex rings movie
Colliding vortex rings movie

Exam papers. Hardcopies of solutions for the speciman exam paper can be obtained from me later in the semester. We will discuss this in week 10 during the usual lecture times.


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 28th
Hanging rope Feb 4th
Central force field + Spherical pendulum Feb 11th
None---midterm this day. Feb 18th
Channel shear flow + steady oscillating channel flow Feb 25th
Hurricane + Clepsydra Mar 11th
Fourier series: questions 1 + 3 Mar 18th
Heat equation: questions 1 + 2 Mar 25th


This webpage and its content was started on 26/1/2009.

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: 27/3/2014.

simonm [at] ma.hw.ac.uk