PHY1033 : Introduction to Calculus
- Offered for Year: 2023/24
- Module Leader(s): Dr Michael White
- 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 |
|---|---|---|---|---|---|
| Guided Independent Study | Assessment preparation and completion | 30 | 1:00 | 30:00 | Completion of in course assessments |
| Scheduled Learning And Teaching Activities | Lecture | 11 | 1:00 | 11:00 | Problem Classes |
| Scheduled Learning And Teaching Activities | Lecture | 31 | 1:00 | 31:00 | Formal Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures |
| Scheduled Learning And Teaching Activities | Small group teaching | 5 | 1:00 | 5:00 | Group Tutorials |
| Guided Independent Study | Independent study | 121 | 1:00 | 121:00 | N/A |
| Total | 200:00 |
Jointly Taught With
| Code | Title |
|---|---|
| MAS1605 | Introduction to Calculus |
Teaching Rationale And Relationship
The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.
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 | 120 | 1 | A | 80 | N/A |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises | 1 | M | 5 | Problem-solving exercises assessment |
| Prob solv exercises | 1 | M | 5 | Problem-solving exercises assessment |
| Prob solv exercises | 1 | M | 5 | Problem-solving exercises assessment |
| Prob solv exercises | 1 | M | 5 | Problem-solving exercises assessment |
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of programme accreditation.
Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.
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.
Reading Lists
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- PHY1033's Timetable