Undergraduate Programme and Module Handbook 2010-2011 (archived)

# Module MATH1561: SINGLE MATHEMATICS A

## Department: Mathematical Sciences

### MATH1561: SINGLE MATHEMATICS A

Type | Open | Level | 1 | Credits | 20 | Availability | Available in 2010/11 | Module Cap | None. | Location | Durham |
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#### Prerequisites

- Normally, A level Mathematics at grade C or better, or equivalent.

#### Corequisites

- None.

#### Excluded Combination of Modules

- Core Mathematics A (MATH1012), Mathematics for Engineers and Scientists (MATH1551) and Foundation Mathematics (MATH1641) may not be taken with or after this module.

#### Aims

- This module has been designed to supply mathematics relevant to students of the physical sciences.

#### Content

- Basic functions and elementary calculus: including standard functions and their inverses, the Binomial Theorem, basic methods for differentiation and integration.
- Complex numbers: including addition, subtraction, multiplication, division, complex conjugate, modulus, argument, Argand diagram, de Moivre's theorem, circular and hyperbolic functions.
- Single variable calculus: including discussion of real numbers, rationals and irrationals, limits, continuity, differentiability, mean value theorem, L'Hopital's rule, theory of integration, Taylor's theorem.
- Numerical methods: including number representation and errors, iteration schemes and convergence, numerical integration.
- Matrices and determinants: including determinants, rules for manipulation, cofactors, transpose, adjoint and inverse matrices, Cramer's rule, Gaussian elimination, eigenvalues and eigenvectors, symmetric matrices.

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will: be able to solve a range of predictable or less predictable problems in Pure and Numerical Mathematics.
- have an awareness of the basic concepts of theoretical mathematics in these areas.
- have a broad knowledge and basic understanding of these subjects demonstrated through one or more of the following topic areas: Elementary algebra.
- Calculus.
- Complex numbers.
- Taylor's Theorem.
- Numerical methods.
- Linear equations and matrices.

Subject-specific Skills:

Key Skills:

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

- Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
- Initial diagnostic testing fills in gaps related to the wide variety of syllabuses available at Mathematics A-level.
- Tutorials provide the practice and support in applying the methods to relevant situations as well as active engagement and feedback to the learning process.
- Summative weekly coursework provides an incentive for students to consolidate the learning of material as the module progresses (there are no higher level modules in the department of Mathematical Sciences which build on this module). It serves as a guide in the correct development of students' knowledge and skills, as well as an aid in developing their awareness of standards required.
- The end-of-year written examination provides a substantial complementary assessment of the achievement of the student.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 60 | 3 per week | 1 Hour | 60 | |

Tutorials | 20 | Weekly | 1 Hour | 20 | ■ |

Preparation and Reading | 120 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 90% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Written examination | 3 hours | 100% | Yes |

Component: Coursework | Component Weighting: 10% | ||

Element | Length / duration | Element Weighting | Resit Opportunity |

One written assignment each teaching week | 100% | Completing the May/June exam paper over the summer, to be returned by the beginning of the resit exam period |

#### Formative Assessment:

45 minute collection paper in the first week of Epiphany term.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University