Week 7
We continued looking at “The Engineer’s Transform” — the Laplace Transform.
We continued looking at partial fractions and then the inverse Laplace Transform.
We had one tutorial Wednesday PM where we worked on partial fractions.
Week 8
It is my intention to record lectures at home. I have a camcorder and a whiteboard in my home office.
I am going to, more or less as soon as possible, record at home enough lectures for you to be able to do the second assignment. This means I want to push forward up to p.132.
I expect ye to watch the lectures and to spend some time doing exercises. How much time you devote to exercises is up to you, but in theory you are supposed to spend 7 hours per week on MATH7021 between classes and independent learning.
It certainly will not be a waste of your time to work on the following exercises:
- p.114 (fifth answer is wrong)
- p.123, Q. 1, 7, 8, 10
Also:
- p.86, Q. 1-5
- p. 91, Q. 1-7
- p. 86, Q. 6
Obviously as we don’t have tutorial time my instruction is to send me on screen shots of your work to which I will provide feedback.
Assignment 2
Assignment 2 had a hand-in time and date of 18:00, 2 April: the Thursday of Week 10. Assignment 2 is in the manual.
Unfortunately we have not completed enough material for me to expect you to be able to do the Assignment at this time.
You could do:
- p. 169, Q. 1 (c)
- p. 173, Q. 1
Hopefully following some video lectures ye can begin this assessment as normal.
Study
Please feel free to ask me questions about the exercises via email or even better on this webpage.
Student Resources
Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc.
Undetermined Coefficients
Only those of us who finished Assignment 1 early got much tutorial time with Chapter 2. I will hope that we will get more tutorial time on Chapter 2 at a later date, but until then, I have developed the following for you to practise your differentiation which you need for Chapter 2 here:
Gaussian Elimination Tutor
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.
J.P. McCarthy: Math Page 
2 comments
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March 18, 2020 at 2:50 pm
Student
About the Q. 4-6 on p. 123, when I use “complete the square” for the function I don’t know what to do next. For example, with:
March 18, 2020 at 3:08 pm
J.P. McCarthy
You have not seen these examples yet but will this week.
First of all, video is coming. Watch, e.g. minutes 2.00 – 11.55 and 25.45 – 27.35 (there is more coming).
Let me talk through this specific example.
O.K. When you look at
you think that it looks like
Except it is ‘shifted’, the
is shifted to 
. So 
is more like:
See this
on ‘top’? You need this. Change the 
to achieve this:
Of course this changes
. To ‘balance the books’ you must also add one:
Now this can be split up:
This first term is a ‘shifted’
. We can deal with this later.
We have a problem with
To be a shifted
it must be of the form:
By looking at the ‘bottom’
, we know that 
but we have instead one on top. We want a two… so put a two there:
Of course this is not correct. We have changed this function… we have multiplied by two… to fix it we must also divide by two or multiply by one half:
Now everything is in order:
This is a shifted
plus half a shifted 
.
The First Shift Theorem says that:
In English, for shifted functions, bring them back as normal (
), and then multiply by an exponential shift (
). Here 
and so the exponential shift is 
. This is the usual “if 
come back as 
we see with the inverse Laplace Transform of 
.
So
is a shifted 
plus half a shifted 
so its inverse Laplace Transform is:
Regards,
J.P.