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PHY1033 : Introduction to Calculus

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 ActivitiesLecture331:0033:00Formal Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture111:0011:00Problem Classes – Synchronous On-Line
Scheduled Learning And Teaching ActivitiesLecture51:005:00Group Tutorials – Present in Person
Guided Independent StudyAssessment preparation and completion301:0030:00Completion of in course assessments
Guided Independent StudyIndependent study1211:00121:00N/A
Total200:00
Jointly Taught With
Code Title
MAS1605Introduction 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 Examination1201A80N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M10Problem-solving exercises
Prob solv exercises1M10Problem-solving exercises
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