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MATH1081: Calculus I (Maths Hons)

Please ensure you check the module availability box for each module outline, as not all modules will run in each academic year. Each module description relates to the year indicated in the module availability box, and this may change from year to year, due to, for example: changing staff expertise, disciplinary developments, the requirements of external bodies and partners, and student feedback.

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

Prerequisites

  • 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 of Modules

  • 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

ActivityNumberFrequencyDurationTotalMonitored
Lectures583 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 Hour58 
Tutorials9Weeks 3, 5, 7, 9 (Term 1) and 13, 15, 17, 19 (Term 2), plus 1 revision tutorial in Easter term.1 Hour9Yes
Problems Classes4Fortnightly in weeks 14-201 Hour4 
Support classes18Weekly in weeks 2-10 and 12-201 Hour18 
Preparation and Reading111 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 90%
ElementLength / DurationElement WeightingResit Opportunity
Written Examination3 hours100
Component: Continuous AssessmentComponent Weighting: 10%
ElementLength / DurationElement WeightingResit Opportunity
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

More information

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