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Mathematics 1FM (MATH 10520)

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Administrative Information

  1. Unit number and title: MATH 10520 Mathematics 1FM
  2. Level: C/4 (Open)
  3. Credit point value: 20 credit points
  4. Year: 12/13
  5. First Given in this form: 2008/2009
  6. Unit Organiser: Carl Dettmann
  7. Lecturer: Dr Carl Dettmann
  8. Teaching block: 2
  9. Prerequisites: Equivalent standard of GCSE grade C plus International Foundation Programme diagnostic test

Unit 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.

 

General Description of the Unit

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.

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.

Teaching Methods

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.

 

Learning Objectives

At the end of the unit students should be able to:

  • use numerical methods to find areas under curves, etc.
  • integrate simple functions and know the physical meaning of the integral.
  • work with functions of two or more variables
  • manipulate and use matrices
  • use vectors 

Assessment Methods

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

Calculators of an approved type (non-programmable, no text facility) are allowed. From 2012-13 ONLY calculators carrying a 'Faculty of Science approved' sticker will be allowed in the examination room.

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.

Award of Credit Points

To be awarded the credit points for this unit you must normally pass the unit, i.e. you must achieve an assessment mark of 40 or more.

The assessment mark is calculated as described in the Assessment section above. Details of the university's common criteria for the award of credit points are set out in the Regulations and Code of Practice for Taught Programmes at http://www.bristol.ac.uk/esu/assessment/codeonline.html

In particular, for this unit:

  • students are expected to attend all the relevant tutorials,
  • students are expected to hand in attempts every week to the weekly exercises set.

Note: we will make allowances for illness and other such good reasons, PROVIDED that you follow the School of Mathematics procedures: you must inform the Undergraduate Student Administrators in Mathematics and submit a completed Extenuating Circumstances form (available from the School) together with supporting written documentation (e.g. a doctor's certificate, specifying the date(s) you were unable to undertake academic work).

 

Transferable Skills

  • Increased skills in handling mathematics and data of all kinds (numeracy skills).
  • IT skills developed through use of MAPLE

Texts

Recommended (but not required) textbook:

  • Understanding Pure Mathematics, A.J. Sadler and D.W.S. Thorning (Oxford University Press 1995)

You may also find the following books helpful:

  • Help yourself to algebra, Hugh Neill (Longman 1996)
  • Mind the Gap, bridging the gap between GCSE and AS Maths, Roger Cahalin, Alessandra Desbottes & Suzanne Doyle (Coordination Group Publications 2002)

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.

Advice for Students

Maths 1FM is intended to teach you something useful that you will use in your subsequent honours studies. You must take it seriously and not just concentrate on your language studies. A third of your time in teaching block 2 should be spent on mathematics, and bear in mind that this time includes practical sessions in your other subjects. (Working at mathematical problems is similar to working in the laboratory.) 

The topics covered are closely related to the A level syllabus, and the first required book is an A level text; see the Texts section. If at a future date you need to go further into mathematics, then you can get other books, or look in the library for similar texts containing many worked examples. In addition, you will probably need to practise your basic algebraic manipulative skills. For this it is recommended that you purchase and work through exercises in the book Help yourself to algebra by Hugh Neill.

Practice is essential if you are to become competent in basic skills. Problems will be set each week, which you must hand in. You are not discouraged from working together (problems that have been worrying you for days can often be solved very quickly in discussion with your friends). But you must hand in your own write-up, even if it is based on ideas that may have been discussed with other people. Handing in identical pieces of work is not acceptable.

Tutorials in groups of about 12 to 15 students will be held weekly. You are expected to attend and talk about the material being covered. Problems not set to be handed in can be attempted during the tutorial, and any other problems raised. In the first week the tutorial time will be used to introduce you to the MAPLE software (see below).

There are 3 lectures each week as well as the tutorials.  If in doubt, ASK - that is what lecturers and tutors are for. Don't assume everyone else knows what is going on - if you don't understand something, other people probably don't either, and will appreciate your asking about it. 

If you find that you still have problems unsolved at any time, please ask for extra help.

Calculators

Don't feel that you have to buy a graphics calculator - they are not essential, and graphic calculators may not be used in the examination. An ordinary scientific calculator (cost £5 to £10) is sufficient, but you should check that it satisfies our requirements on calculators used in examinations:

  • no graphics capability
  • no complex number or matrix or symbolic algebra or calculus capability
  • no equation-solving capability
  • no capacity to store text
  • no programming capability.