This is an archived handbook for a previous year. The current undergraduate and postgraduate handbooks can be viewed using the links above.

Undergraduate Handbook 2025-2026 (archived)

Module MATH1081: Calculus I (Maths Hons)

Department: Mathematical Sciences

MATH1081: Calculus I (Maths Hons)

Type	Level	Credits	Availability	Module Cap	Location
Tied	1	20	Available in 2025/2026	None.	Durham

Tied To

Pre-requisites

Normally, A level Mathematics at grade A or better and AS level Further Mathematics at grade A or better, or equivalent.

Corequisites

Linear Algebra I (Maths Hons) (MATH1091)

Excluded Combinations

Calculus I (MATH1061), Linear Algebra I (MATH1071), Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571) may not be taken with or after this module.

Aims

This module is designed to follow on from, and reinforce, A level mathematics.
It will present students with a wide range of mathematics ideas in preparation for more demanding material later.
Aim: to introduce crucial basic concepts and important mathematical techniques.

Content

A range of topics are treated each at an elementary level to give a foundation of basic definitions, theorems and computational techniques.
A rigorous approach is expected.
Elementary functions of a real variable.
Limits, continuity, differentiation and integration.
Ordinary Differential Equations.
Taylor series and Fourier series.
Calculus of functions of many variables
Partial differential equations and method of separation of variables
Fourier transforms

Learning Outcomes

Subject-specific Knowledge

By the end of the module students will: be able to solve a range of predictable or less predictable problems in Calculus,
have an awareness of the basic concepts of theoretical mathematics in Calculus,
have a broad knowledge, and a basic understanding and working knowledge of each of the subtopics,
have gained confidence in approaching and applying calculus to novel problems.

Subject-specific Skills

Students will have enhanced skills in the following areas: modelling, spatial awareness, abstract reasoning and numeracy.

Key Skills

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
Tutorials provide active engagement and feedback to the learning process.
Weekly homework problems provide formative assessment to guide students in the development of their knowledge and skills. They also aid the development of students' awareness of the required standards of rigour.
Initial diagnostic testing and associated supplementary problems classes fill in gaps related to the wide variety of syllabuses available at Mathematics A-level, and provide extra support to the course.
The examination provides a final assessment of the achievement of the student.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total Hours	Attendance Monitored
Lectures	58	3 per week in terms 1, 2 or 3 per week in term 2 (alternating fortnightly with Problems Classes), 2 revision lectures in term 3.	1 Hour	58
Tutorials	9	Weeks 3, 5, 7, 9 (Term 1) and 13, 15, 17, 19 (Term 2), plus 1 revision tutorial in Easter term.	1 Hour	9	Yes
Problems Classes	4	Fortnightly in weeks 14-20	1 Hour	4
Support classes	18	Weekly in weeks 2-10 and 12-20	1 Hour	18
Preparation and Reading				111
Total				200

Summative Assessment

Component	Component Weighting	Element	Length/Duration	Element Weighting	Resit Opportunity
Examination	90%	Written Examination	3 hours	100%
Continuous Assessment	10%	Fortnightly electronic assessments during the first 2 terms. Normally, each will consist of solving problems. Students will have about one week to complete each assignment.		100%

Formative Assessment

40 minute collection paper in the beginning of Epiphany term. Fortnightly formative assessment

Students who do not attend monitored activities shown under Teaching Methods and Learning Hours, or who fail to complete the summative or formative assessment(s) specified above, may be subject to the Academic Progress procedures defined in the University's General Regulation V, and may be required to leave the University.