Undergraduate Programme and Module Handbook 2010-2011 (archived)

# Module MATH1571: SINGLE MATHEMATICS B

## Department: Mathematical Sciences

### MATH1571: SINGLE MATHEMATICS B

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

- A level Mathematics at Grade C or better, or equivalent.

#### Corequisites

- Single Mathematics A (MATH1561).

#### Excluded Combination of Modules

- 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

- Vectors: including scalar and vector products, derivatives with respect to scalars, two-dimensional polar coordinates.
- Ordinary differential equations: including first order, second order linear equations, complementary functions and particular integrals, simultaneous linear equations, applications.
- Fourier analysis: including periodic functions, odd and even functions, complex form.
- Functions of several variables: including elementary vector algebra (bases, components, scalar and vector products, lines and planes), partial differentiation, composite functions, change of variables, chain rule, Taylor expansions.
- Partial differential equations: including simple examples of partial differential equations, methods of solution: change of variables, separation of variables.
- Multiple integration: including double ant triple integrals, line integrals, Green's theorem.
- Introduction to probability: including sample space, events, conditional probability, Bayes' theorem, independent events, random variables, probability distributions, expectation and variance.

#### 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 Applied 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: Vectors.
- Ordinary differential equations.
- Fourier analysis.
- Partial differential equations.
- Functions of several variables.
- Probability.

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 | 66 | 3 per week | 1 Hour | 66 | |

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 to by the start 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