Undergraduate Programme and Module Handbook 2024-2025

# Module MATH1061: Calculus I

## Department: Mathematical Sciences

### MATH1061: Calculus I

Type | Open | Level | 1 | Credits | 20 | Availability | Available in 2024/2025 | Module Cap | None. | Location | Durham |
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#### Prerequisites

- Normally, A level Mathematics at grade A or better and AS level Further Mathematics at grade A or better, or equivalent.

#### Corequisites

- Linear Algebra I (MATH1071)

#### Excluded Combination of Modules

- Calculus I (Maths Hons) (MATH1081), Linear Algebra I (Maths Hons) (MATH1091), Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571) may not be taken with or after this module.

#### Aims

- This module is designed to follow on from, and reinforce, A level mathematics.
- It will present students with a wide range of mathematics ideas in preparation for more demanding material later.
- Aim: to introduce crucial basic concepts and important mathematical techniques.

#### Content

- A range of topics are treated each at an elementary level to give a foundation of basic definitions, theorems and computational techniques.
- A rigorous approach is expected.
- Elementary functions of a real variable.
- Limits, continuity, differentiation and integration.
- Ordinary Differential Equations.
- Taylor series and Fourier series.
- Calculus of functions of many variables
- Partial differential equations and method of separation of variables
- Fourier transforms

#### 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 Calculus,
- have an awareness of the basic concepts of theoretical mathematics in Calculus,
- have a broad knowledge, and a basic understanding and working knowledge of each of the subtopics,
- have gained confidence in approaching and applying calculus to novel problems.

Subject-specific Skills:

- Students will have enhanced skills in the following areas: modelling, spatial awareness, abstract reasoning and numeracy.

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.
- Tutorials provide active engagement and feedback to the learning process.
- Weekly homework problems provide formative assessment to guide students in the development of their knowledge and skills. They also aid the development of students' awareness of the required standards of rigour.
- Initial diagnostic testing and associated supplementary support classes fill in gaps related to the wide variety of syllabuses available at Mathematics A-level, and provide extra support to the course.
- The examination provides a final assessment of the achievement of the student.

#### Teaching Methods and Learning Hours

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

Lectures | 58 | 3 per week in terms 1, 2 or 3 per week in term 2 (alternating fortnightly with Problems Classes), 2 revision lectures in term 3. | 1 Hour | 58 | |

Tutorials | 9 | Weeks 3, 5, 7, 9 (Term 1) and 13, 15, 17, 19 (Term 2), plus 1 revision tutorial in Easter term. | 1 Hour | 9 | ■ |

Problems Classes | 4 | Fortnightly in weeks 14-20 | 1 Hour | 4 | |

Support classes | 18 | Weekly in weeks 2-10 and 12-20 | 1 Hour | 18 | |

Preparation and Reading | 111 | ||||

Total | 200 |

#### Summative Assessment

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

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

Written Examination | 3 hours | 100% | Yes |

Component: Continuous Assessment | Component Weighting: 10% | ||

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

Fortnightly electronic assessments during the first 2 terms. Normally, each will consist of solving problems. Students will have about one week to complete each assignment. | 100% |

#### Formative Assessment:

40 minute collection paper at the beginning of Epiphany term. Fortnightly formative assessment.

■ 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