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Faculty Handbook 2019-2020

# Module Description

Please ensure you check the module availability box for each module outline, as not all modules will run each academic year.

## Department: Mathematical Sciences

### MATH1061: Calculus I

Type Level Credits Availability Module Cap Location Open 1 20 Available in 2019/20 None. Durham

#### 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 (MATH1071)

#### Excluded Combination of Modules

• 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.
• 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 Contact 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: 100%
Element Length / duration Element Weighting Resit Opportunity
Written examination 3 hours 100% Yes
Component: Component Weighting: %
Element Length / duration Element Weighting Resit Opportunity
%

#### 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