| Unit name | Mathematics 1FM |
|---|---|
| Unit code | MATH10520 |
| Credit points | 20 |
| Level of study | C/4 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Dr. Chenchiah |
| Open unit status | Not open |
| Pre-requisites | |
| Co-requisites | |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
The unit develops integral calculus, differential equations, vectors and matrices roughly from GCSE to A level standard, bearing in mind the needs of students of the sciences.
Aims:
To introduce integral calculus, differential equations, vectors and matrices as useful tools. This unit is primarily for International Foundation Programme students seeking to study science or other numerate subjects in the future.
Syllabus
Algebra & Calculus Numbers in brackets refer to weeks
E2 Vectors and Calculus: 15 lectures (13) Areas by Summation: Mid-ordinate rule, Trapezium rule, Area under curve, Fundamental Theorem of Calculus
(14) Integration: Integration of polynomials; Definite & indefinite integrals
(15-17) Vectors: Definition of vector; Notation; Addition; Multiplication by scalar; Scalar product; Distributive rule; Use of i, j, k; Angle between vectors in 2-D & 3-D; Proof of Pythagoras; Formula for cos(A+B) only. Vector equations of lines and planes. Vector perpendicular to two given vectors.
E3 Matrices and Calculus: 18 Lectures
First order differential equations; solution by separation of variables. Simple second order linear equations, oscillations, application of complex numbers. Functions of two variables, surfaces, contour lines. Partial derivatives, second derivatives, simple applications.
Simultaneous linear equations, revision of 2x2 systems, solution of 3x3 systems. Matrix notation, addition and multiplication, transpose. Determinants; matrix inverse. Square matrix as transformation in the plane or space. Introduction to eigenvalues.
Relation to other units:
There is another unit for students taking the Foundation year programme: Mathematics 1FS. It is identical to this unit for the first 5 weeks. In weeks 18 onwards, Mathematics 1FS has statistics while Mathematics 1FM has more mathematics.
At the end of the unit students should be able to:
Transferable Skills:
3 lectures per week, with weekly tutorials. Marked work is returned to the students and difficulties explained in the tutorials.
The MAPLE software is used in the algebra and calculus part of the course.
You should realise that if you fail the unit, or fail to gain the credit points, the consequences may be very serious. You may not be granted a certificate.
To pass the unit your final assessment mark must be 40 or over. This assessment mark will be made up as follows:
100% from an examination in May/June (details below).
In addition weekly work will be marked.
Details of the Summer Examination Candidates in Maths 1FM examinations may use calculators of approved type (no graphics, text facility or symbolic algebra, non-programmable).
The final examination in May/June consists of one paper, of three hours. The examination paper has two sections. Section A has 10 short questions, all of which should be answered; it carries 40% of the marks for the paper. Section B has three longer questions, of which you should do TWO. If you do more than two, your best two answers will be used for assessment. Section B carries 30% of the marks on the paper and examines material in E2. Section C has three longer questions, of which you should do TWO. If you do more than two, your best two answers will be used for assessment. Section C carries 30% of the marks on the paper and examines material in E3.
September Examination
If you fail Mathematics 1FM in June, you may (depending on which programme you are on and how you have done in your other units) be allowed to resit it in September. The September examination paper has the same structure as in June.
Recommended (but not required) textbook:
You may also find the following books helpful:
