- Offered for Year: 2022/23
- 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
Teaching Activities
| Category |
Activity |
Number |
Length |
Student Hours |
Comment |
|---|
| Scheduled Learning And Teaching Activities | Lecture | 33 | 1:00 | 33:00 | Formal Lectures – Present in Person |
| Scheduled Learning And Teaching Activities | Lecture | 11 | 1:00 | 11:00 | Problem Classes – Synchronous On-Line |
| Guided Independent Study | Assessment preparation and completion | 30 | 1:00 | 30:00 | Completion of in course assessments |
| Scheduled Learning And Teaching Activities | Small group teaching | 5 | 1:00 | 5:00 | Group Tutorials – Present in Person |
| Guided Independent Study | Independent study | 121 | 1:00 | 121:00 | N/A |
| Total | | | | 200:00 | |
Jointly Taught With
| Code |
Title |
|---|
| PHY1033 | Introduction to Calculus |
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.
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 | 80 | N/A |
Exam Pairings
| Module Code |
Module Title |
Semester |
Comment |
|---|
| PHY1033 | Introduction to Calculus | 1 | N/A |
Other Assessment
| Description |
Semester |
When Set |
Percentage |
Comment |
|---|
| Prob solv exercises | 1 | M | 10 | n/a |
| Prob solv exercises | 1 | M | 10 | n/a |
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments 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.
In the event of on-campus examinations not being possible, an on-line alternative assessment will be used for written examination 1.
Reading Lists
Timetable
