MAS1605 : Introduction to Calculus
- Offered for Year: 2020/21
- Module Leader(s): Dr Stuart Hall
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
| Semester 1 Credit Value: | 20 |
| ECTS Credits: | 10.0 |
Aims
To lay the foundations of calculus for more advanced mathematical study. Students will learn about functions and limits. Students will be able to describe and compute limits of sequences and series, determine whether a function is continuous and/or differentiable, compute derivatives and integrals using standard techniques.
Module summary
Virtually every branch of mathematics and statistics can be developed only from a firm foundation. These skills form the toolkit required for further study.
A clear understanding and appreciation of many fundamental topics is required, primarily, those of algebra and calculus.
This module concentrates on the foundations of calculus. Of course, understanding alone is not sufficient: considerable manipulative skill is an essential ingredient if progress is to be made. This module provides a basis for all this, by building on the ideas explored in A-level (or equivalent) studies, with the ideas rehearsed - often in a different, but more complete way.
Outline Of Syllabus
Methods of proof: induction
Inequalities
Sequences and limits.
Completeness and Cauchy sequences
Functions: limits, continuity and differentiability, elementary functions.
Differentiation: definition, rules, properties, higher derivatives.
Integration: Riemann sums, methods of integration.
Series: convergence and tests, Maclaurin and Taylor series.
Teaching Methods
Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Guided Independent Study | Assessment preparation and completion | 30 | 1:00 | 30:00 | Completion of in course assessment |
| Structured Guided Learning | Lecture materials | 36 | 1:00 | 36:00 | Non synchronous activities |
| Scheduled Learning And Teaching Activities | Lecture | 9 | 1:00 | 9:00 | Synchronous On Line Material |
| Structured Guided Learning | Structured non-synchronous discussion | 18 | 1:00 | 18:00 | Non synchronous discussion to support learning |
| Scheduled Learning And Teaching Activities | Workshops | 9 | 1:00 | 9:00 | Present in Person |
| Scheduled Learning And Teaching Activities | Drop-in/surgery | 4 | 1:00 | 4:00 | Office hour or discussion board activity |
| Guided Independent Study | Independent study | 94 | 1:00 | 94:00 | Preparatory time for lectures, background reading, coursework review |
| Total | 200:00 |
Teaching Rationale And Relationship
Non-synchronous online materials are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on assessed work. Present-in-person and synchronous online sessions are used to help develop the students’ abilities at applying the theory to solving problems and to identify and resolve specific queries raised by students, and to allow students to receive individual feedback on marked work. Students who cannot attend a present-in-person session will be provided with an alternative activity allowing them to access the learning outcomes of that session. In addition, office hours/discussion board activity will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.
Alternatives will be offered to students unable to be present-in-person due to the prevailing C-19 circumstances.
Student’s should consult their individual timetable for up-to-date delivery information.
Assessment Methods
Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.
The format of resits will be determined by the Board of Examiners
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Written exercise | 1 | M | 20 | n/a |
| Written exercise | 1 | M | 20 | n/a |
| Written exercise | 1 | M | 60 | Alternative assessment |
Assessment Rationale And Relationship
The course assessments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.
Reading Lists
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- MAS1605's Timetable