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Mathematics 1EM (MATH 10600)

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Administrative Information

  1. Unit number and title: MATH 10600 Mathematics 1EM
  2. Level: C/4 (Open)
  3. Credit point value: 40 credit points
  4. Year: 12/13
  5. First Given in this form: 2002/2003
  6. Unit Organiser: Isaac Chenchiah
  7. Lecturer: Dr. Isaac Chenchiah, Dr. Carl Dettmann
  8. Teaching block: 1 and 2
  9. Prerequisites: GCSE grade C or better.

Unit aims

To revise elementary mathematics in GCSE (bearing in mind the needs of students who have not studied mathematics for 2 years or more). To introduce basic algebra, trigonometry, calculus, differential equations and matrices as useful tools for science students.

General Description of the Unit

The unit develops algebra, elementary calculus, differential equations 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 without A level mathematics: Mathematics 1ES. It is identical to this unit for most of the first 17 weeks. In weeks 18 onwards, Mathematics 1ES has statistics while Mathematics 1EM 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. To assist students in evaluating their progress, short tests are held in weeks 5 and 9.

Learning Objectives

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

  • perform basic algebraic manipulations
  • sum arithmetic and geometric series
  • solve linear, simultaneous linear, and quadratic equations
  • use numerical methods to find areas under curves, etc.
  • use trigonometry and vectors
  • differentiate and integrate simple functions and know the physical meaning of the derivative and integral.
  • work with functions of two or more variables
  • manipulate and use matrices

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 allowed to continue in your degree programme. You should consult your Faculty Handbook or your departmental information.

To pass the unit your final assessment mark must be 40 or over. This assessment mark will be made up as follows:

  • 10% from the midsessional examination in January,
  • 90% from examinations in May/June (details below).

To assist students in evaluating their progress, short tests are held in weeks 5 and 9.

Summer Examinations

Candidates in Maths 1EM examinations may use calculators. Only calculators of 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 2 papers, each of three hours. Paper 1 contributes 40% of the final mark for the unit. Paper 2 contributes 50% of the final mark for the unit. 

  • Paper 1 has two sections. Section A has 10 short questions, all of which should be answered; it carries 40% of the marks for this paper.  Section B has 6 longer  questions, of which you should do FOUR. If you do more than four, your best four answers from this section will be used for assessment. Section B carries 60% of the marks for this paper. Paper 1 examines E1.
  • Paper 2 has three sections. Section A has 10 short questions, all of which should be answered; it carries 40% of the marks for this paper. Section B has 3 longer  questions, of which you should do TWO. If you do more than two, your best two answers from this section will be used for assessment. Section B carries 30% of the marks for this paper. Section C has 3 longer  questions, of which you should do TWO. If you do more than two, your best two answers from this section will be used for assessment. Section C carries 30% of the marks for this paper. Section A examines work from E2 and E3. Section B examines work from E2. Section C examines work from E3.

January examinations

The Mid-sessional January Progress Examinations are right at the start of the second term. This term begins on Friday 11th January 2013, and the examination for this unit may be on Friday 11th January or Saturday 12th January. IT IS YOUR RESPONSIBILITY to ensure that you are in Bristol to sit the examination; otherwise your mark will be zero (unless you have a certified illness or other special circumstances of which the school has been notified). You will be notified of the date, time and place of the January examination before the end of the first term.

These examinations are compulsory: you must attend. Your mark in the January examination for the unit will contribute 10% to the final assessment mark for the unit in June. It should also give you, and us, an indication of how well you are coping with the unit.

The one-and-a-half hour examination paper for Mathematics 1EM contains two sections. Section A has 5 short questions, all of which should be answered; it carries 40% of the marks for the paper. Section B has 3 longer questions, of which you should do TWO. If you do more than two, your best two answers will be used for assessment; it carries 60% of the marks for this paper. This examination will contribute 10% to the final assessment of the unit in June and it should also give you, and us, an indication of how well you are coping with the unit.

September Examinations

If you fail Mathematics 1EM in June, you may (depending on which Faculty you are in and how you have done in your other units) be allowed to resit it in September. The September examination papers have 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 must attend the January examination,
  • 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).

Texts

Many textbooks cover the material taught in this unit, for example:

  • 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

Numbers in brackets refer to weeks.
 
I Algebra & Differential Calculus: 36 Lectures
 
(1&2) Algebra: Terminology and priorities of operations; Function notation and evaluation; Laws of indices; Gathering like terms; Expansions; Factorisation; Linear equations; Linear inequalities; Changing the subject of formulae; Equation of straight line; Algebraic fractions; Factorisation & solution of quadratics; Factorising polynomials.
 
(3&4) Calculus: Gradient of curve as limit of chord; Derivatives of powers of x and polynomials; Tangents and Normals; Chain Rule; Product and Quotient Rules; Stationary points; Second derivative and testing for max/min/point of inflexion; Optimisation problems.
 
(5&6) Growth functions, exponentials & logarithms: Exponential growth and decay; Logarithms; Derivatives of exponential and logarithmic functions; Compound interest.
 
(7) Sequences & Series: Generating sequences by formulae or inductive rules; Arithmetic Progressions; Geometric Progressions; Applications.
 
(8) Circles and pairs of straight lines: Circles: Equations; Finding centre and radius from equation; Whether lines cut or miss, whether points lie inside or outside; Simultaneous linear equations, including cases with no/many solutions.
 
(9-11) Trigonometric Functions: Definition of sin, cos and tan; Graphs; Inverses; Simple trignometric equations; Arc length & sector area; Limit of (sin x)/x; Sine and Cosine rules; Differentiation of trigonometric functions; Implicit differentiation.

(12) Complex Numbers: Definition in the form a + ib; r (cos A + i sin A); multiplication; the Argand diagram.

II Integral Calculus & Vectors: 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).Vector equations of lines and planes. Vector perpendicular to two given vectors.
 
III Differential Equations, multivariable Calculus & Matrices: 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 1EM is intended to teach you something useful that you will use in your honours subjects. You must take it seriously and not just concentrate on your honours subject. A third of your time 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.) You will not be allowed to continue studying your Honours subject unless you obtain 40 credit points from this course; see the Award of Credit Points section for more details.

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.

There are 3 lectures each week as well as the tutorials. In weeks 5 and 9 there will be short tests. You will take the tests during the tutorial period. Completion of these tests may be required for the award of credit points.

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.