F1.2UE2 Differential equations and linear algebra

• Introduction
• Announcements
• Electronic resources
• Module timetable

Introduction

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

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

Lectures. Monday 2:15pm (NS136), Tuesday 1:15pm (NS301) and Thursday at 1:15pm (WP108).

Tutorials. One a week: Tuesday at 2:15pm (NS301).

Webpages. This course homepage where you can download lecture notes, further handouts, solutions to the exercises, Maple or Mathematica worksheets and other stuff is:

http://www.ma.hw.ac.uk/maths/modules/F12UE2

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

Course aims and objectives. The course aims to provide an introduction to those aspects of linear mathematics needed in science and engineering.

Syllabus.

• Linear differential equations with constant coefficients. Solution of linear second order, constant coefficient, ordinary differential equations with polynomial, exponential or trigonometric inhomogeneities. The auxiliary equation, complementary function, particular integral (via the method of undetermined coefficients) and the general solution. Resonance. Equidimensional equations.
• Laplace Transforms. Calculation of simple Laplace transforms, inverse transforms. Derivative, shift and convolution theorems. Applications to solving differential equations.
• Systems of linear algebraic equations. Augmented matrices, elementary row operations. Gaussian elimination method. Row-echelon form. Rank of a matrix. Inverting a matrix.
• Linear algebraic eigenvalue problems. Eigenvalues and eigenvectors. Diagonalization of real symmetric matrices. Applications to solving differential equations.

Assessment. The continuous assessment consists of the specified exercises at the end of chapters 1--7, 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).

Together the continuous assessment will count for 15 percent of the final mark. There is a two-hour final exam at the end of term which counts for 85 percent of the course mark.

There is a resit in August/September 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.

Contract. Students are expected to read the notes in the accompanying 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 assessed and non-assessed exercises at the end of chapters 1--7 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 or during the office hours. 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 main two main recommended books are Kreyszig and Meyer (see the bibliography of the main notes for details).

Useful webpages. An interesting webpage that you might find useful is

http://www.eg.bucknell.edu/~dcollins/teaching/2004Spring/Phys222