MAS 214 LINEAR OPERATORS and DIFFERENTIAL EQUATIONS 2005/2006

Lecturer: Prof. I. Goldsheid, Maths Room 254.

Lectures: Monday 9.00-10.00 Math. Building; 11.00-12.00,.Engineering 237

Tuesday 13.00-14.00, Engineering 324

Exercise Class: Tuesday 15.00-16.00 in Geography, room 216 starting on 17^th January.

Exercises will be handed out via internet, beginning on January 12. Solutions must be placed in the green box in the basement. The due time will be indicated at each problem sheet. There will be at least 8 sets of exercises in total.

Office hours: Thursday 12.00-14.00 in Room Maths 254.

Books: There is no compulsory course-book, but the following books may prove useful:

"Mathematical Methods of Physics" by Matthews and Walker (Benjamin);

"Principles and Techniques of Applied Mathematics" by Friedman (Dover).

Course Assessment.

End-of-year Examination (duration 2 hours) will contribute 80% of the final mark for the course.

The rubric will be as follows:

This paper has two Sections and you should attempt both Sections. Please read carefully the instructions given at the beginning of each Section.

Calculators are not permitted in this examination. The unauthorised use of a calculator constitutes an examination offence.

Section A: You should attempt ALL questions. Marks awarded are shown next to the question

Section B: Each question carries N marks. You may attempt all questions. Except for the award of a bare pass, only marks for the best TWO questions will be counted.

Coursework: weekly exercises will contribute a total of 10 marks towards the final mark for the course, the best 5 solutions counting 2 marks each.

Mid-term test: will contribute 10% of the final mark for the course. It will be held in the 7th week of term on Tuesday 21^st February at 1 p.m. in Engineering 324.

Important: those failing to submit reasonable attempt to at least six problem sheets or showing poor results in the test may not be allowed to take the final exam.

Key Objectives

(A) Understand what is meant by an orthonormal basis of vectors or functions, and be able to calculate the coefficients involved when expressing an arbitrary vector or function as a linear combination of members of such a set.

(B) Be able to determine the eigenvalues and eigenfunctions of a simple integral and of a simple differential operator with specified domain.

(C) Understand what is meant by the Green’s function of a given second order differential equation, understand the technique for calculating it, and be able to implement this technique for suitable differential operators.

(D) Know how to use the method of "separation of variables" to solve simple second order linear homogeneous partial differential equations with suitably specified boundary conditions.