I am emailing a link of this to everyone on the class list every week. 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.com and I will add you to the mailing list.

## Continuous Assessment

You are identified by the last four digits of your student number unless you are winning the league. The individual quiz marks are out of 2.5 percentage points. Your best eight quizzes go to the 20% mark for quizzes. The R % column is your running percentage (for best eight quizzes), MPP is your Maple Percentage Points and the GPP is your Gross Percentage Points (for best eight quizzes and Maple). Most of the columns are rounded but column nine, for quiz eight, is correct.

 S/N Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 R % QPP MPP GPP Kelliher 2.5 2.5 2.5 2.5 2.3 2.5 2.5 2.5 99 19.8 7.5 27.3 8335 2.375 2.5 2.4 2.5 2.5 2.5 2.3 2.5 98 19.6 7.5 27.1 3281 2.4 2.5 2.5 2.5 2.1 2.5 2.5 2.5 98 19.5 7.5 27.0 5527 1.9 2.5 2.5 2.5 2.5 2.5 2.5 2.5 97 19.4 7.5 26.9 4198 0 1.2 2 2.5 1.7 2.5 2.5 2.5 85 14.9 7.5 22.4 8478 1.9 1.72 2.15 2.4 0 2.5 2 2.2 85 14.9 7.5 22.4 8416 2.3 1 2.2 2.5 2.5 1.2 2.4 2.5 83 16.6 7.5 24.1 8403 1.85 1.4 2.45 2.5 1.3 2.4 1.9 2.5 82 16.3 7.5 23.8 7878 2.15 2.2 2.25 1.9 2.1 1.5 1.9 1.9 80 15.9 7.5 23.4 6548 1.55 1 2.25 2.5 1.6 2.3 2.1 2.5 79 15.8 7.5 23.3 1864 1.3 2.4 2.5 2.1 1.24 1.1 2.4 2.5 78 15.5 7.5 23.0 8556 1.35 0.6 2.4 2.2 0 2 2.5 2.5 77 13.6 7.5 21.1 8603 0.6 1.8 1.85 2.4 0 2.4 2.5 1.6 75 13.2 7.5 20.7 2567 1.55 1.5 2.05 1.28 1.8 2.1 2.1 2.2 73 14.6 7.5 22.1 7950 0 0 0.8 0 1.8 1.2 2.5 2.5 70 8.8 6 14.8 2859 2.4 1 0 0.5 1.6 1.7 1.9 2.5 66 11.6 7.5 19.1 5546 0 0 1.1 1 1.9 1.5 2.5 1.9 66 9.9 7.5 17.4 1852 0.7 1.2 1.6 1.5 2.1 2.2 0.9 1.3 58 11.5 7.5 19.0 8455 0.2 0.9 1.05 0.7 1.9 2.2 2 1 50 10.0 7.5 17.5 9464 1.2 0.9 1.5 0.9 1.24 0.8 2.1 0 49 8.6 6 14.6 7209 1.9 1.2 1.75 0.5 0.16 0 0 0 44 5.5 4.5 10.0 4775 0.5 0.3 1 0 0.4 1.2 1.9 1.9 41 7.2 7.5 14.7 5553 0.4 0.8 0 0 0.1 0 0 0 17 1.3 4.5 5.8

Any students who missed a Maple lab are invited to do the relevant lab in their own time and send their Maple file to me via email.

## Quiz 9 Question Bank

• P.97, Q. 2,3,4,5
• P.106, Q. 1

The answer to Q.1 (vi) has a mistake — instead of 12 & 4 it should be 9 & 3.

Note that P.106 Q.1 (ii) and (vi) are actually the same but the solution to Q. 1(ii) is flawed (the edited answer to part (vi) above is correct).

Here I give a proper solution for part (ii)/(vi).

We have $f(t)=3\cos(4t)\sin(2t)$. Now using the identity

$\displaystyle 2\cos A\sin B=\sin(A+B)-\sin(A-B),$

which gives

$\displaystyle \cos A\sin B=\frac{1}{2}\sin(A+B)-\frac{1}{2}\sin(A-B)$,

we have

$\displaystyle 3\cos(4t)\sin(2t)=3\left(\frac{1}{2}\sin(6t)-\frac{1}{2}\sin(2t)\right)$

$\displaystyle =\frac32 \sin(6t)-\frac32\sin(2t)$,

which can be transformed linearly (term-by-term, pulling out constants) using the tables:

$\displaystyle F(s)=\mathcal{L}\{f(t)\}=\frac{3}{2}\frac{6}{s^2+36}-\frac{3}{2}\frac{2}{s^2+4}$

$\displaystyle =\frac{9}{s^2+36}-\frac{3}{s^2+4}$.

There is no value in writing down the final answers alone — you will receive marks for full and correct solutions — but nothing for final answers without justification or skipping important steps. Please don’t learn off model solutions — you need to understand the material not just on a superficial level to do well later on. Quiz 9 runs from 19:00 to 19:15 sharp on Wednesday 22 April as it is not a ‘Maple’ night.

## Week 9

In Week 9 we continued our work on Laplace Transforms.

## Week 10

We have a busy night in Week 10. We will do more examples of taking a differential equation, translating/transforming it into an algebraic equation and solving this transformed equation for the transform of the solution of the original differential equation, $\mathcal{L}\{f(t)\}$. Then we will learn how to send this back to $f(t)$ using the Inverse Laplace Transform. To do these we will need partial fractions so we will have a quick review of these. Then we will do loads of examples of Inverse Laplace transforms.

## Maple Test

The Maple Test will take place on the night of 29 April. I have given ye a sample in class.

Group 1 – Starts at 18:00 and Finishes at 20:50:

• Wednesdays 18:00-19:05 – Maple Test in room C219
• Wednesdays 19:15-19:30 – Weekly Quiz in C212
• Wednesdays 19:30-20.50 – Theory class in room C212

Group 2 – Starts at 19:15 and Finishes at 22:00:

• Wednesdays 19:15-19:30 – Weekly Quiz in C212
• Wednesdays 19:30-20:50 – Theory class in room C212
• Wednesdays 20.55-22:00 – Maple Test in room C219

As you can see here you can download a student copy of Maple. Some students said that they were unable to open the file I sent in their Maple 17 — this is strange as I am actually using Maple 16!

The word on the Academic Learning Centre is that although the evening session perhaps might have been made exclusive to evening students, the fact of the matter is that they are not.

My departmental head suggested that if a group of ye want to get an improvement in your ALC experience, that ye should email questions to catherine.palmer@cit.ie in advance of the session. Dr Palmer said that this will allow her to more easily help ye.

## Study

Please feel free to ask me questions about the exercises via email or even better on this webpage. Anyone can give me exercises they have done and I will correct them. I also advise that you visit the Academic Learning Centre.

## Continuous Assessment

The Continuous Assessment is broken into Weekly Quizzes (20%) and Maple (10%). There will be eleven weekly quizzes and your eight best results will count (so 2.5% per quiz from eight quizzes). You will receive an email (i.e. this one) on Thursday/Friday detailing the examinable exercises. Maple consists of five labs and a Maple Test in the sixth lab. Satisfactory participation in labs gives you 1.5% and the Maple Test is worth 2.5%. More on this in the coming days.