MAU22203/MAU33203 - Analysis in Several Real Variables
Course Information
Lecturer: Adam KeilthyMAU22203 Assessment: 20% homework assignments, 80% final exam.
MAU33303 Assessment: 10% homework assignments, 90% final exam.
The course will not follow any particular textbook, but students may find the following options helpful. Be aware that most of these contain far more than we can realistically hope to cover in this course.
- Calculus on manifolds by M.Spivak
- Foundations of Modern Analysis by J. Dieudonne
- Advanced calculus of several variables by C.H. Edwards
Lecture notes
This section will be populated with notes from the lectures as the course goes on. Please report any errors or typos you find so that I can correct them quickly.The current (mostly complete) lecture notes can be found here, last updated 19/11/24
Homework problems
You must submit your homework assignments before the deadline, preferably by emailing it to me, but you are welcome to submit a physical copy after a lectureWhere possible, please submit your assignment as a single PDF file, with your name in the filename, e.g. adam_keilthy_RAHW1.pdf or similar. Please also ensure that your name is visible on the first page of the assignment.
I encourage you to typeset your work in LaTeX. Doing so will increase your mark by 20% (but it will still be capped at 100/100). A rough template that does not reflect best practice or prettiest practice can be found here
The solutions will be made available immediately after the deadline, so late submissions cannot be accepted
| Exercise sheet | Due date | Solutions |
|---|---|---|
| Sheet 1 | Friday October 4th, 2PM | Solutions 1 |
| Sheet 2 | Sunday November 3rd, 23:59 | Solutions 2 |
| Sheet 3 | Sunday November 24th, 23:59 | Solutions 3 |
Sheets will be released approximately two weeks prior to the deadline.
The fourth exercise sheet is entirely optional, and has a relatively short deadline. If you choose to complete and submit it, your continuous assessment will be based on the best 3 out of 4 homeworks submitted.
| Exercise sheet | Due date | Solutions |
|---|---|---|
| Sheet 4 | Sunday December 1st, 23:59 | Solutions 4 |
Tutorial Problem Sets
The current plan is to replace one Friday lecture a fortnight with a tutorial, assuming there is sufficient time. If there is another problem you would like to discuss, please email me in advance of the class. In multi-part exercises, not every part will necessarily be addressed.. If there are any results or example from class you would like us to look over, please let me know in advance. If there are any problems from a textbook you would like us to look at, you are welcome to suggest the problem.Solutions will be made available shortly after the tutorials.
| Tutorial sheet | Solutions | Tutorial date |
|---|---|---|
| Sheet 1 | Solutions 1 | Friday 20th September |
| Sheet 2 | Solutions 2 | Friday 4th October |
| Sheet 3 | Solutions 3 | Friday 18th October |
| Sheet 4 | Solutions 4 | Friday 15th November |
Sample Exams
Below are two sample exams, with complete solutions for one of them. The actual exam will be the same format. Be aware that some of the questions in these sample exams are more time consuming than is reasonable for an actual examSample exam 1 and its solutions
Sample exam 2 and its solutions