Unit name | Mathematics 1A20 |
---|---|

Unit code | MATH11004 |

Credit points | 20 |

Level of study | C/4 |

Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |

Unit director | Professor. Porter |

Open unit status | Open |

Pre-requisites |
A level in Mathematics or equivalent |

Co-requisites |
None |

School/department | School of Mathematics |

Faculty | Faculty of Science |

This unit is designed for students with A-level mathematics who want a 20 credit-point unit on mathematical techniques. It consists of the first 12 weeks of MATH10100, Mathematics 1AM, covering calculus. There is no other mathematics unit which can be taken as a sequel to this unit.

**Aims:**

To consolidate, develop and extend the skills in single variable calculus introduced at A level.

**Syllabus**

The numbers of lectures (shown in brackets) are a rough guide only.

- General introduction, Review of algebra and trigonometry. (2)

- Functions and graphs: important examples, inverse functions. (2)

- Sequences and series; limits of functions; continuous functions (3)

- Exponential function; natural logarithm; hyperbolic functions (2)

- Complex numbers; Argand diagram, polar form, complex exponential, complex roots (4)

- Differential calculus, differentiability, basic methods, higher derivatives, Leibniz formula; differentiation of inverse functions (3)

- Taylor approximations; Taylor series; convergence of the series; ratio test for power series; applications of Taylor series: maxima and minima; l'Hospital's rule for limits (4)

- Integration: integrals as antiderivatives and as area; standard techniques; infinite integrands; infinite ranges of integration. (4)

- Differential equations: 1st-order separable and first order linear differential equations. (2)

- 2nd order linear differential equations with constant coefficients, homogenous including simple harmonic motion, inhomogeneous including resonance. (4)

- Full-range Fourier series in [-pi, pi] and general intervals. (4)

**Relation to Other Units**

This unit consists of the first half of the 40cp units Mathematics 1AM/1AS.

After taking this unit, students should have a thorough grasp of one-variable calculus and complex numbers, including simple differential equations and Fourier Series.

Transferable Skills:

Mathematical techniques for application in the physical sciences.

The unit is based on lectures, problems classes and tutorials on how to apply the techniques of the calculus in solving problems.

The lecturer will distribute problem sheets based on the work done in lectures, and will set specific problems which you will be required to hand in. During the first few weeks, weekly problems classes will be held and work handed in centrally. Later the problems classes will be replaced by weekly tutorials and work will be handed in to tutors for marking.

Experience shows that progress in mathematics depends crucially on regular work at examples. For this reason you are REQUIRED to attend tutorials and to hand in the set work. See the section Formal Requirements of the Unit below.

The final assessment mark for Mathematics 1A20 is calculated as follows:

- 10% from a midsessional examination in January,
- 90% from an examination in May/June.

More information is given below.

Use of Calculators and Notes Candidates may bring into the examination room a calculator of the approved type (briefly: no graphics, programming, text storage, complex numbers, matrices, or symbolic algebra).

Candidates may bring into the examination room one A4 sheet of notes; both sides of the sheet may be used.

Details of the Summer Examination The summer examination lasts 3 hours, and is in 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 assessed. Section B carries 60% of the marks for this paper.

**January examinations**

The January midsessional examinations are right at the start of the second term. This term begins on Friday 13th January 2012, and the Maths 1A20 examination may be on Friday 13th January or Saturday 14th 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). You will be notified of the date, time and place of the January examination before the end of the first term.

The midsessional written examination lasts 1 1/2 hours, and is in two sections:

- Section A has 5 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 assessed. Section B carries 60% of the marks for this paper.

**September examinations**

If you fail this unit 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 paper has the same structure as in June. If you are offered a resit, you must take the resit examination.

The following book is recommended, but it is not essential.

- Jordan, D.W. & Smith, P. Mathematical Techniques: An introduction for the engineering, physical, and mathematical sciences (4th edition), Oxford University Press, Oxford, 2008.

**Supplementary Booklist**

These are alternative texts. They should be available in the library, and you may find them useful in different ways, as discussed below.

- Stewart, J., Calculus - Early Transcendentals, Brooks/Cole

A very clearly written and comprehensive introduction to calculus, going beyond the Maths 1AM course. Includes vectors but not matrices. Recommended. There are many similar textbooks in the library.

- Gilbert, J. and Jordan, C., Guide to Mathematical Methods, Palgrave (Macmillan) 2002.

Introduces topics in a fairly elementary way, but does not cover all the material.

- Berry, J., Northcliffe, A., & Humble, S., Introductory mathematics through science applications, Cambridge University Press, Cambridge.

Introduces topics in a fairly elementary way. May be useful if you feel you need to strengthen your basic skills.

- Boas, M.L., Mathematical methods in the physical sciences, Wiley,

Useful for the second-year physics course: you may find it too demanding at the beginning of the 1AM course.

- Jeffrey, A., Mathematics for engineers and scientists, Chapman & Hall, London

Covers most of the syllabus, and a good deal more besides, in a terse style..

- Jeffrey, A., Essentials of engineering mathematics, Chapman & Hall, London

Similar in style to the previous book, though with slightly less extensive coverage.