Unit name | Calculus 1 |
---|---|

Unit code | MATH11007 |

Credit points | 20 |

Level of study | C/4 |

Teaching block(s) |
Teaching Block 4 (weeks 1-24) |

Unit director | Dr. Tourigny |

Open unit status | Not open |

Pre-requisites |
A at A-level Mathematics or equivalent |

Co-requisites |
None |

School/department | School of Mathematics |

Faculty | Faculty of Science |

Unit aims

To provide some basic tools and concepts for mathematics at the undergraduate level, by

- developing and extending the calculus skills introduced at A level

- linking the material taught in Calculus to that of Analysis, Linear Algebra and Mechanics

General Description of the Unit

Calculus is based on the calculus learnt at school. It will develop a deeper understanding, a stronger grasp of the techniques, and further topics that are not included in A level syllabuses. This includes in particular the extension of methods of calculus to functions of two or more variables. The logical foundations of calculus are not included in this unit; they are developed in the companion unit Analysis. The course will concentrate more on general ideas and methods, rather than rigorous logical development.

Relation to Other Units

The material taught in this unit is linked to that of the following other units

- MATH11005 (linear Algebra and Geometry) develops an abstract framework which emcompasses some of the objects developed in Calculus. For instance, one may view functions or gradients as "vectors", and solution sets of some differential equations as "vector spaces".
- MATH11006 (Analysis) is a completely rigorous treatment of (some of) the material presented in the Calculus unit.
- MATH11009 (Mechanics), as the unit that deals with some of the consequences of Newton's laws of motion, provides countless applications of Calculus.
- MATH12001 (Computational Mathematics) which discusses the implementation on computers of many techniques developed in calculus.
- MATH11300 (Probability) uses the tools of Calculus (e.g. integration, power series etc.) to study discrete and continuous random variables.

Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/

Learning Objectives

After taking this unit, students should

- be able to evaluate and manipulate derivatives and integrals with ease;
- be able to solve some simple first and second order differential equations;
- be able to use partial derivatives and the gradient vector;
- be familiar with vectors in 2 and 3 dimensions;
- be familiar with some standard curves and surfaces, and be able to work with them;
- be able to evaluate line integrals;
- understand the connection between Calculus on the one hand and Analysis, Probability and Mechanics on the other.

Transferable Skills

Problem-solving skills.

Lectures, exercises to be done by students, tutorials.

100% Examination

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

The recommended text is:

The recommended text is: Schaum's Outline of Calculus (Fourth Edition), by Frank Ayres Jr and Elliott Mendelson. Schaum's Outline Series, McGraw-Hill, 1999. ISBN 0-07-041973-6