- Offered for Year: 2019/20
- Module Leader(s): Dr Kate Henderson
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
|
Semester 1 Credit Value:
|
15
|
|
ECTS Credits:
|
8.0
|
Aims
To lay the foundations of the 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 which is 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
Sequences and limits.
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
Teaching Activities
| Category |
Activity |
Number |
Length |
Student Hours |
Comment |
|---|
| Scheduled Learning And Teaching Activities | Lecture | 1 | 1:00 | 1:00 | Assignment laboratory |
| Guided Independent Study | Assessment preparation and completion | 1 | 2:00 | 2:00 | Practise for must-pass computer test |
| Scheduled Learning And Teaching Activities | Lecture | 1 | 1:00 | 1:00 | Class test |
| Guided Independent Study | Assessment preparation and completion | 1 | 2:00 | 2:00 | Must-pass computer test |
| Scheduled Learning And Teaching Activities | Lecture | 3 | 1:00 | 3:00 | Problem classes |
| Scheduled Learning And Teaching Activities | Lecture | 3 | 1:00 | 3:00 | Revision lectures |
| Scheduled Learning And Teaching Activities | Lecture | 34 | 1:00 | 34:00 | Formal lectures |
| Guided Independent Study | Assessment preparation and completion | 1 | 9:00 | 9:00 | Revision for class test |
| Guided Independent Study | Assessment preparation and completion | 1 | 16:30 | 16:30 | Revision for unseen exam |
| Guided Independent Study | Assessment preparation and completion | 1 | 2:30 | 2:30 | Unseen exam |
| Scheduled Learning And Teaching Activities | Small group teaching | 5 | 1:00 | 5:00 | Small group tutorials |
| Scheduled Learning And Teaching Activities | Drop-in/surgery | 4 | 1:00 | 4:00 | Tutorials in the lecture room |
| Scheduled Learning And Teaching Activities | Drop-in/surgery | 24 | 1:00 | 24:00 | Office hours/self-study: Studying, practising and gaining understanding of course material |
| Guided Independent Study | Independent study | 4 | 1:00 | 4:00 | Preparation for small group tutorials |
| Guided Independent Study | Independent study | 5 | 3:00 | 15:00 | Review of coursework assignments and course test |
| Guided Independent Study | Independent study | 4 | 6:00 | 24:00 | Preparation for coursework assignments |
| Total | | | | 150:00 | |
Teaching Rationale And Relationship
Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer. The small group tutorials allow students to improve their understanding of fundamental material and to develop mathematical presentation skills.
Assessment Methods
The format of resits will be determined by the Board of Examiners
Exams
| Description |
Length |
Semester |
When Set |
Percentage |
Comment |
|---|
| Written Examination | 150 | 1 | A | 70 | N/A |
| Written Examination | 40 | 1 | M | 10 | Class test |
Exam Pairings
| Module Code |
Module Title |
Semester |
Comment |
|---|
| MAS1601 | Introduction to Calculus | 1 | N/A |
Other Assessment
| Description |
Semester |
When Set |
Percentage |
Comment |
|---|
| Prob solv exercises | 1 | M | 6 | Coursework assignments |
| Prob solv exercises | 1 | M | 6 | Small group |
| Prof skill assessmnt | 1 | M | 4 | Presentation to small group - 5 minutes |
| Computer assessment | 1 | M | 2 | CBA 1 |
| Computer assessment | 1 | M | 2 | CBA 2 |
Zero Weighted Pass/Fail Assessments
| Description |
When Set |
Comment |
|---|
| PC Examination | M | Must pass test |
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module, as this is the best way to test understanding of the Physics content. The coursework assignments will consist of one written assignment (approximately 3%), and one assignment laboratory (approximately 3%. The coursework assignments and the (in class, therefore 40 minute) test 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. The small group work involves approximately five meetings with a group leader who assesses each student on their contributions to group discussions on solving exercises (6%) and on a 5 minute individual presentation (4%). There is a computer test on basic material which students must pass in order to pass the module.
Reading Lists
Timetable
