MAS221 Analysis 2019-2020

Semester 2

Lecturer: Prof Sarah Whitehouse

Novel Coronavirus (COVID-19) disruption

From 16 March 2020, the university has suspended face-to-face teaching. The latest information for students is here:

The situation is changing rapidly and you should check back regularly for updates, as well as checking your university email account.

Teaching is now online. There will be no lectures or tutorials face-to-face for this module (or any other) and students should not come to teaching rooms until further notice.

Some teaching materials will appear here and on MOLE.

Semester dates have been amended. It's currently Easter break, with the semester resuming on 20 April.

This is the 2019-2020 course web page for semester 2 of MAS221 Analysis. For official course information, including timetabling, please consult the list of current modules.

Here is a link to the semester one webpage.

Semester 2 Course Information

A good grasp of Semester 1 material is essential to understanding the material in Semester 2.  This semester we will continue the study of analysis of functions of one variable, building on what we covered in Semester 1.  


90% by exam at the end of Semester 2, 10% is based on coursework, 5% for each semester.

**** Arrangements for Semester 2 coursework and overall assessment are under review, in light of the current situation. ****

Homework 1 has been handed-in, is being marked and will count. This will not be returned individually, but detailed general feedback is coming soon.

I expect a further online test to go ahead at some point, but the precise details are not known yet. I'll give plenty of notice and time to complete it.

Lecture notes

In Semester 1 we got as far as proving the Intermediate Value Theorem. We began Semester 2 at that point - please refer to the Semester 1 lecture notes.

Here are the full notes to the end of Chapter 4.

Here are the outline lecture notes for the rest of semester 2. As in semester 1, this is a version without proofs of theorems or worked solutions to examples. A fuller version including these materials is now available below. Note however that I usually draw lots of graphs and diagrams on the blackboards in the lectures and many of these are not in the notes. I am investigating the best way to convey that information in the light of suspension of face-to-face teaching.

Here are the full notes for Semester 2. This is what I expected to cover in a usual year. It is not clear at present how much of this material will be covered.

Here are the slides from Chapter 5 onwards. These match the outline notes in content.


Semester 1 problems (repeated here for convenience, as we did some chapter 4 problems at the start of semester 2)
Semester 2 problems

Problem classes

These take place on Tuesdays (at 11 or 2) in weeks 2, 4, 6, 8, 10 and 12.
****No classes in week 6 and until further notice.****

Week 2 problems: Chapter 4, Qs 60, 65; Chapter 5, Qs 79, 80, 85.
Week 4 problems: Chapter 5, Qs 86, 89, 90.

Please use the Discussion Forum on MOLE to ask questions.

Homework schedule

Details of questions set:

Homework 1 (worth 1% credit for a reasonable attempt): the week 2 problems
Chapter 4, Qs 60, 65; Chapter 5, Qs 79, 80, 85.
Revised hand-in date: Thursday lecture in week 3, 27th February.

No further homework hand-in deadlines for the moment, but please work on the questions below.

Chapter 5, Qs 86, 89, 90.

If you have already done those questions, please try some questions from the 2017-18 exam paper. You have seen all the material needed for Q1, Q2 and part (i) of Q3.

Semester 2 online test: to be confirmed.


Solutions to the problems will appear here as the module progresses.

Solutions up to Q85.


There are various ways students can get feedback on their individual work and their progress on this module. The most important is the feedback from the markers on the homework assignments. The markers put in considerable time and effort, which is wasted if marked homework is not collected back and reviewed. Understanding and acting on this feedback is a key way to improve - likely to result in an improved performance on the exam far out-weighing the 1% for the homework itself. Online tests also provide some feedback and so does the help available in tutorial classes. With the suspension of face-to-face teaching, the discussion forum on MOLE will provide a place to ask questions.

Exam information

Some more detailed exam information will appear here in due course.

Link to the 2017-18 paper and the general past papers page.

Solutions to two papers:

MAS221 exam 2017-18 - solutions [ There were some small changes to terminology in relation to domains of functions. In Q4b), the Greek letter chi χ was used as notation for indicator functions. This year we are using 1 instead. ]

MAS221 exam 2016-17 - solutions  [ Q4 parts (iii), (iv), (v) are on material that will not be covered this year. ]

Office hour

Suspended until further notice. Please see the discussion forum on MOLE and feel free to ask questions there.

Contact Details

Prof Sarah Whitehouse
Room J6c, Hicks Building
Telephone: 0114 2223870  (internal extension: 23870)

Last updated: 30 March 2020