MA1RA2NU-Real Analysis II

Module Provider: Mathematics and Statistics
Number of credits: 20 [10 ECTS credits]
Level:4
Semesters in which taught: Semester 1 module
Pre-requisites:
Non-modular pre-requisites: High School Mathematics
Co-requisites: MA1LANU Linear Algebra
Modules excluded:
Current from: 2022/3

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

Type of module:

Summary module description:

This module covers core topics in calculus.

The Module lead at NUIST is DrTemesgen Leta (leta_temesgen@163.com).  

Aims:

To build on and develop students' understanding of pre-university mathematics, especially the calculus and to extend this into two or more dimensions. Techniques of solution of ordinary differential equations of the first and second order, and simple applications will also be presented. Emphasis will be placed on appreciation of the real-world applications of such mathematics.

Assessable learning outcomes:

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

1. Learn the theory of improper integral and its computational skills and commonly used criterion for the test of convergence.


2. Learn the theory of series, including number series and function series.


3. Learn the theory of functions with several variables, including the limit, continuity, differentiation, Taylor expansion, extreme and so on.


4. Learn basic theory for implicit function and computation of differentiation for implicit function and some applications.


5. Learn basic theory for integrals of several variables or integral with parameter.


6. Be able to compute integrals of several variables and integrals for curve and curved surface.

Additional outcomes:

Students will acquire some appreciation of real-world applications of their mathematics.

Outline content:

This module reinforces and extends the calculus topics encountered in school courses. Its objectives are to introduce some of the basic "tools of the trade" and to develop the skills required to solve a range of problems using these tools. Methods are developed intuitively rather than by means of rigorous proofs. Applications of the various techniques will be given.

Brief description of teaching and learning methods:

Lectures supported by problem sheets and tutorials.

Contact hours:

	Semester 1	Semester 2
Lectures	74
Guided independent study:
Wider reading (independent)	62
Wider reading (directed)	24
Exam revision/preparation	30
Advance preparation for classes	10
Total hours by term	200	0
Total hours for module	200

Summative Assessment Methods:

Method	Percentage
Written exam	70
Class test administered by School	30

Summative assessment- Examinations:

3 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: https://www.reading.ac.uk/cqsd/-/media/project/functions/cqsd/documents/cqsd-old-site-documents/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 re-examination paper of 3 hours duration in August - 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 including the in-class test).

Additional Costs (specified where applicable):

1) Required text books: 

2) Specialist equipment or materials: 

3) Specialist clothing, footwear or headgear: 

4) Printing and binding: 

5) Computers and devices with a particular specification: 

6) Travel, accommodation and subsistence: 

Last updated: 22 September 2022