I am emailing a link of this to everyone on the class list every Friday afternoon. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.ie and I will add you to the mailing list.
Test 1
Consider this notice for the test on Thursday 25 October at 8.20 p.m (just under two weeks away) (I have spoken with Ted and I think there is going to be making a change to his assignment so for now we are full speed ahead for Week 6. Note that there is still a small chance that this will be held in Week 7 Thursday 1 November at 8.20 p.m.).
Please find a sample test. I will give ye a copy of this Thursday night which will include the Finite Differences table and the Laplace Transform tables.
Note that the format will be the same as this.
- Forward Difference Methods (14 marks)
- Gaussian Elimination Methods including Partial Pivoting 7 marks)
- The Jacobi and Gauss-Siedel Method (7 marks)
- Laplace Transforms (7 marks)
Q. 4 will be covered Thursday night.
J.P. McCarthy: Math Page 
2 comments
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October 19, 2012 at 4:42 pm
Student 22
You have written
but should this not be 
as you wrote in a previous example.
October 19, 2012 at 4:51 pm
J.P. McCarthy
I must have a made a mistake in the previous page because we usually want to write the Laplace transform as
rather than 
to distinguish it easily from 
.
Recall that the Laplace Transform is a mapping that ‘eats’ functions of single (positive real) variable
and ‘spits out’ functions of a single (complex) variable 
. If we write ![[\mathbb{R^+}\rightarrow\mathbb{R}]_{t}](https://s0.wp.com/latex.php?latex=%5B%5Cmathbb%7BR%5E%2B%7D%5Crightarrow%5Cmathbb%7BR%7D%5D_%7Bt%7D&bg=ffffff&fg=545454&s=0&c=20201002)
for the set of functions of a single positive real variable 
and ![[\mathbb{C}\rightarrow \mathbb{C}]_{s}](https://s0.wp.com/latex.php?latex=%5B%5Cmathbb%7BC%7D%5Crightarrow+%5Cmathbb%7BC%7D%5D_%7Bs%7D&bg=ffffff&fg=545454&s=0&c=20201002)
for the set of functions of a single complex variable 
then we might write
In this example we could have been more careful and explicit and wrote that
is the solution of the differential equation.
Now finally, rather than carry around the messy
— the Laplace Transform of 
(in this case the Laplace Transform of the solution of the differential equation), we just use the notation
Regards,
J.P.