Skip to main content


MAS1605 : Introduction to Calculus

  • Offered for Year: 2023/24
  • Module Leader(s): Dr Stuart Hall
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus

Your programme is made up of credits, the total differs on programme to programme.

Semester 1 Credit Value: 20
ECTS Credits: 10.0
European Credit Transfer System


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


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 ActivitiesLecture111:0011:00Problem Classes
Scheduled Learning And Teaching ActivitiesLecture311:0031:00Formal Lectures
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures
Guided Independent StudyAssessment preparation and completion301:0030:00Completion of in course assessments
Scheduled Learning And Teaching ActivitiesSmall group teaching51:005:00Group Tutorials
Guided Independent StudyIndependent study1211:00121:00N/A
Jointly Taught With
Code Title
PHY1033Introduction 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

Description Length Semester When Set Percentage Comment
Written Examination1501A80N/A
Exam Pairings
Module Code Module Title Semester Comment
Introduction to Calculus1N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M20n/a
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