Durham University
Programme and Module Handbook

Undergraduate Programme and Module Handbook 2023-2024 (archived)

Module MATH1081: Calculus I (Maths Hons)

Department: Mathematical Sciences

MATH1081: Calculus I (Maths Hons)

Type Tied Level 1 Credits 20 Availability Available in 2023/24 Module Cap None. Location Durham
Tied to G100
Tied to G103
Tied to G111
Tied to G114

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 Combination 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

    Activity Number Frequency Duration Total/Hours
    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 14 Weekly in weeks 2-10, fortnightly in weeks 13-19, and one in week 21. 1 Hour 14 ■
    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 106
    Total 200

    Summative Assessment

    Component: Examination Component Weighting: 90%
    Element Length / duration Element Weighting Resit Opportunity
    Written Examination 3 hours 100% Yes
    Component: Continuous Assessment Component Weighting: 10%
    Element Length / duration Element Weighting Resit Opportunity
    Fortnightly electronic assessments during the first 2 terms. Normally, each will consist of solving problems and will typically be one to two pages long. 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

    ■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University