Undergraduate

modules

Modules

MAS1601 : Introduction to Calculus

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 ActivitiesLecture341:0034:00Formal lectures
Guided Independent StudyAssessment preparation and completion19:009:00Revision for class test
Guided Independent StudyAssessment preparation and completion119:0019:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:302:30Unseen exam
Scheduled Learning And Teaching ActivitiesLecture11:001:00Assignment laboratory
Guided Independent StudyAssessment preparation and completion21:002:00Practice for Pass/Fail tests
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class test
Guided Independent StudyAssessment preparation and completion21:002:00Pass/Fail tests
Scheduled Learning And Teaching ActivitiesLecture31:003:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture31:003:00Revision lectures
Scheduled Learning And Teaching ActivitiesSmall group teaching51:005:00Small group tutorials
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Tutorials in the lecture room
Guided Independent StudyIndependent study121:3021:30Studying, practising and gaining understanding of course material
Guided Independent StudyIndependent study53:0015:00Review of coursework assignments and course test
Guided Independent StudyIndependent study46:0024:00Preparation for coursework assignments
Guided Independent StudyIndependent study41:004:00Preparation for small group tutorials
Total150:00
Jointly Taught With
Code Title
PHY1031Introductory 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. 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 Examination1501A70N/A
Exam Pairings
Module Code Module Title Semester Comment
PHY1031Introductory Calculus1N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M10Coursework assignments
Prob solv exercises1M10Coursework test
Prob solv exercises1M6Small group work
Prof skill assessmnt1M4Presentation to small group
Zero Weighted Pass/Fail Assessments
Description When Set Comment
PC ExaminationMTest on fundamental material
PC ExaminationMTest on fundamental material
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments will consist of one written assignment (approximately 3%), one assignment laboratory (approximately 3%) and two computer based assessments (each approximately 2%). The coursework assignments and the (in class) coursework 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 are thus formative as well as summative assessments. 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 an individual presentation (4%). There are two tests on basic material that do not carry any module assessment weight which students must pass in order to pass the module.

Reading Lists

Timetable