Last year's maths is easy, this year's maths is hard and next year's maths is impossible.
We then did some further study on the Euler Method. The global error with the Euler Method is 
We looked at the Three Term Taylor Method as a better method. To employ the Three Term Taylor Method we need implicit differentiation, which means more pen-and-paper work.
In VBA we finished off the Euler Method Lab 2. Ideally everyone should have done up to p.130.
Some students did or started Exercise 1 and/or Exercise 2 on p. 130.
Read the rest of this entry »This should be started ASAP. This has a provisional hand in time and date of 11:00 Thursday 24 February. Please see Canvas.
We finished Chapter 1 on Monday by looking at applications to temperature distribution, where the Jacobi Method is used to find approximate solutions to a diagonally dominant linear system.
If you want a deep dive into the temperature of a plate stuff there is a post here which explains — in great detail — how the ‘iterations’ are actually physically meaningful.
We had three classes of tutorials — Wednesday and the Thursday double. This means we have had more than five classes of tutorials in the first three weeks.
We are now going to push to complete Chapter 2 over the next two weeks. Any remaining classes will be given over to tutorial time on Chapter 2/1.
I plan to talk about academic integrity for Assignment 1 on Monday, and hopefully do a Chapter 1 “concept MCQ” on Wednesday (technology depending).
Please feel free to ask me questions about the exercises via email or even better on this webpage.
Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..
In theory (see Learner Workload) you are supposed to spend seven hours per week on MATH6040. I know this might not be possible for everyone, but there is no doubt that spending four hours per week on exercises is going to be best for your learning. Any questions, please email.
Please see Canvas —> MATH6040 —> Assignments for more information.
In Week 3 we finished Chapter 1, and the material for Test 1, by talking at the applications of vectors to work and moments
We had an hour and a half of tutorial time on the p.47 and p.40 Exercises.
How much time you put into homework is up to you: of course the more time you put in the better but we all have competing interests. Please feel free to ask me questions about the exercises:
There is an applet to play with:
Additional questions include:
There are more questions to be found in Weeks 1 and 2.
Additional practise questions (beyond the manual) may be found by looking at past MATH6040 exam papers.
We will start at 19:05 with a Vectors Concept MCQ.
We will start looking at Chapter 2: Matrices. We will some examples of matrix arithmetic and look at Matrix Inverses — “dividing” for Matrices. This will allow us to solve matrix equations.
We will likely have no tutorial time.
Please feel free to ask me questions about the exercises via email.
Please see Student Resources for information on the Academic Learning Centre, etc.
We looked at the Euler Method, and then started looking at big 
In VBA we started programming the Euler Method.
Read the rest of this entry »We finished the Gaussian Elimination examples on Monday, and began to look at applications of linear systems to traffic and pipe flow (Thursday).
Someone had an issue with Example 6 on p.26:
This is fixed here (with new additional comments):
We had more than two classes of tutorials — Wednesday and most of the Thursday double.
We will finish the Chapter 1 material and finish the week off with more tutorial time.
Information about Assignment 1 is now up on Canvas.
Please feel free to ask me questions about the exercises via email or even better on this webpage.
Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..
In theory (see Learner Workload) you are supposed to spend seven hours per week on MATH6040. I know this might not be possible for everyone, but there is no doubt that spending four hours per week on exercises is going to be best for your learning. Any questions, please email.
In Week 2 we finished talking about the scalar product before talking about the vector product.
We had about thirty minutes tutorial time on the p. 30 exercises.
How much time you put into homework is up to you: of course the more time you put in the better but we all have competing interests. Please feel free to ask me questions about the exercises:
There are applets to play with:
Additional questions include:
.In Week 3 we will look at the applications of vectors to work and moments
We will manage more tutorial time.
The test will be in Week 5. More official notice will be given in Week 3. There is a sample test on p.56 of the manual.
Please feel free to ask me questions about the exercises via email.
Please see Student Resources for information on the Academic Learning Centre, etc.
In Week 1, by briefly looking at a number of examples (many of which we have seen before), we had a review of some central ideas from approximation theory such as approximation, measurement error, accuracy & precision, iteration, convergence, meshing, error, etc.
We started looking at where ordinary differential equations come into Engineering.
In VBA we had a quick review lab, focussing on plotting data, command buttons, message boxes, input boxes, If-statements and do-loops.
If you have not completed Lab 1 (p.120), I recommend that you do at least up to the first Do-Loop exercise to get you back in the VBA groove.
Read the rest of this entry »We started the first chapter on Linear Algebra. Essentially, for us, simultaneous equations. We looked at Gaussian Elimination including Partial Pivoting, which is required in the presence of rounding. We looked at five examples, and had 15 minutes of tutorial time.
If you download Maple (see Student Resources), there is a Maple Tutor that is easy to use and will help you with Gaussian Elimination. Open up Maple and go to Tools -> Tutors -> Linear Algebra -> Gaussian Elimination.
We will finish the Gaussian Elimination examples on Monday, and maybe begin to look at applications of linear systems to traffic and pipe flow.
We will have a tutorial on Wednesday.
Assignment 1 has a (provisional) hand-in date of Thursday 24 February (Week 5). More information next week once the class list has settled down.
Please feel free to ask me questions about the exercises via email or even better on this webpage.
Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..
In theory (see Learner Workload) you are supposed to spend seven hours per week on MATH6040. I know this might not be possible for everyone, but there is no doubt that spending four hours per week on exercises is going to be best for your learning… but this week’s exercises could be done by you in a matter of minutes.
We began our study of Chapter 1, Vector Algebra by studying the difference between a scalar (single number) and a vector (list of numbers). We looked at how to both visualise vectors and describe them algebraically. We learned how to find the magnitude and direction of a vector, add them and scalar multiply them. We spoke about displacement vectors and introduced the vector product known as the dot product.
How much time you put into homework is up to you: of course the more time you put in the better but we all have competing interests. Please feel free to ask me questions about the exercises:
You could also play with this applet. See the top of p.21 of the manual for details.
In Week 2 we will finish talking about the dot product and we might start talking about the vector product.
If we finish the Vectors chapter in Week 3 the test will be in Week 5 (this is very likely): otherwise we will push this out to Week 6. Official notice will be given in Week 3 (or Week 4 if necessary). There is a sample test on p.56 of the manual.
Please feel free to ask me questions about the exercises via email.
Please see Student Resources for information on the Academic Learning Centre, etc.
Quantum Group Seminar, Monday 24 January, 2022.
Abstract: A classical theorem of Frucht states that every finite group is the automorphism group of a finite graph. Is every quantum permutation group the quantum automorphism group of a finite graph? In this talk we will answer this question with the help of orbits and orbitals.
This talk is based on joint work with Teo Banica.
J.P. McCarthy: Math Page 
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