Undergraduate Programme and Module Handbook 2022-2023 (archived)

# Module PHYS1141: MATHS TOOLKIT FOR SCIENTISTS

## Department: Physics

### PHYS1141: MATHS TOOLKIT FOR SCIENTISTS

Type | Open | Level | 1 | Credits | 20 | Availability | Available in 2022/23 | Module Cap | Location | Durham |
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#### Prerequisites

- A-Level Mathematics

#### Corequisites

- Foundations of Physics 1 (PHYS1122) AND (Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)). Note: This module may only be taken alongside MATH1561 and MATH1571; it may not be taken in a subsequent year.

#### Excluded Combination of Modules

- None

#### Aims

- This module is designed primarily for students studying Department of Physics or Natural Science degree programmes.
- It provides and reinforces the basic mathematical skills required to undertake a degree in Physics and related sciences.
- It provides a large number of practice problems for students transferring from A-level tuition to the independent skills required for a university degree.
- This module complements Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571) which are the standard maths modules taken by most Physics students. MATH1561 and MATH1571 aim to teach new Mathematics material required by physics students in Level 1 and beyond. Maths Toolkit for Scientists aims to equip the students with the skills they need to utilise the Mathematics learnt at A-level.
- The module provides students with practice in the application of mathematics to practical problems.

#### Content

- The syllabus contains:
- Basic algebra, Functions, Polynomial equations, inequalities, partial fractions and proportionality, Logarithms and exponentials, Trigonometry, Further trigonometry, Complex numbers, Matrices and determinants, Using matrices and determinants to solve equations, Vectors, Differentiation, Techniques and applications of differentiation, Integration, Applications of integration, Sequences and series, Differential equations, Functions of more than one variable and partial differentiation.
- Problems in mathematical modelling.

#### Learning Outcomes

Subject-specific Knowledge:

- Students will consolidate their knowledge of key mathematical concepts including basic algebra, trigonometry, linear algebra, vectors and calculus.

Subject-specific Skills:

- The students will obtain expertise in key mathematical skills required at all levels of a physics degree.
- As well as the specific mathematical skills relating to the syllabus content, the students will acquire skills in mathematical manipulation, solving mathematical problems, and the use of key mathematical terms.

Key Skills:

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

- The main mode of teaching will be via independent study â€“ using an on-line database of Mathematics problems.
- This will be supported by regular support workshops and a module leader.
- The on-line database will give the students a large number of basic problems which will improve the studentsâ€™ confidence and expertise in dealing with Mathematics.
- The support workshops will give support to students who are having difficulties.
- In addition, problem solving classes will develop students' skills in the application of mathematics to practical problems.
- The material will be explicitly linked to the contents of a single recommended textbook for the module, thus making clear where students can begin their private study.
- Student performance will be summatively assessed through the on-line problem exercises and one invigilated test.
- The problem exercises and support workshops provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.

#### Teaching Methods and Learning Hours

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

Lectures | 1 | 1 in week 1 | 1 hour | 1 | |

Workshops | 17 | 1 per week | 1 hour | 17 | ■ |

Group Problem Solving Workshops | 8 | 1 per week in term 2 | 1 hour | 8 | ■ |

Private study, preparation and reading | 174 | ||||

Total | 200 |

#### Summative Assessment

Component: Problem exercises | Component Weighting: 80% | ||
---|---|---|---|

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

Problem exercises | 100% | Extended set of further problems | |

Component: Test | Component Weighting: 20% | ||

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

Test | 1 hour | 100% | Test |

#### Formative Assessment:

Problem exercises in the early part of the academic year. Problem solving classes.

■ 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