MA1RA1NU-Real Analysis 1

Module Provider: Mathematics and Statistics
Number of credits: 20 [10 ECTS credits]
Level:4
Terms in which taught: Spring term module
Pre-requisites:
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Current from: 2021/2

Module Convenor: Prof Michael Levitin
Email: m.levitin@reading.ac.uk

Type of module:

Summary module description:

This module provides an introduction to mathematical analysis. We cover contents such as derivatives and differentials, indefinite integrals and definite integrals as well as applications of definite integrals.

The Module lead at NUIST is Dr Chao Wang.

Aims:

To provide a formal introduction to mathematical analysis by rigorously approaching concepts crucial in subsequent analytical topics.

Assessable learning outcomes:

By the end of the module students are expected to be able to:

• Understand the concept of derivatives and calculate derivatives;


• Understand the concept of differentials and manipulate derivatives and differentials of higher order;


• Understand mean value theorems and applications of the derivative;


• Define indefinite integrals and apply techniques of integration;


• Understand c oncept of definite integrals and apply integration techniques to definite integrals;


• Introduce properties of definite integrals and prove some fundamental theorems of calculus;


• Apply definitions & theorems of definite integrals to solve geometrical problems;


• Communicate mathematical arguments.

Additional outcomes:

Outline content:

The module begins with derivatives and differentials, mean value theorems and applications of the derivative, concepts of indefinite integrals and techniques of integration, definite integrals and applications of definite integrals, developing these into a rigorous understanding of calculus.

Brief description of teaching and learning methods:

Lectures supported by problem sheets and tutorials.

Contact hours:

	Autumn	Spring	Summer
Lectures		74
Guided independent study:		126
Total hours by term	0	200	0
Total hours for module	200

Summative Assessment Methods:

Method	Percentage
Written exam	70
Class test administered by School	30

Summative assessment- Examinations:

2 hours

Summative assessment- Coursework and in-class tests:

One examination and a number of class tests.

Formative assessment methods:

Problem sheets.

Penalties for late submission:

The Support Centres will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:

A mark of 40% overall.

Reassessment arrangements:

One examination paper of 2 hours duration in June- the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus coursework marks (70% exam, 30% coursework).

Additional Costs (specified where applicable):

Last updated: 8 April 2021