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MATH1081: Calculus I (Maths Hons)

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Type	Tied
Level	1
Credits	20
Availability	Available in 2024/2025
Module Cap	None.
Location	Durham
Department	Mathematical Sciences

Prerequisites

Normally, A level Mathematics at grade A or better and ASlevel Further Mathematics at grade A or better, orequivalent.

Corequisites

Linear Algebra I (Maths Hons) (MATH1091)

Excluded Combinations of Modules

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

Aims

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

Content

A range of topics are treated each at an elementary levelto give a foundation of basic definitions, theorems and computationaltechniques.
A rigorous approach is expected.
Elementary functions of a real variable.
Limits, continuity, differentiation andintegration.
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 thesubtopics,
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 theapplication of the theory to practical examples.
Tutorials provide active engagement and feedback to thelearning process.
Weekly homework problems provide formative assessment to guidestudents in the development of their knowledge and skills. Theyalso aid the development of students' awareness of the required standardsof rigour.
Initial diagnostic testing and associated supplementaryproblems classes fill in gaps related to the wide variety of syllabusesavailable at Mathematics A-level, and provide extra support to the course.
The examination provides a final assessment of the achievementof the student.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total	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: 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. 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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