## Assignment 1 — Results

I will try and have these for you by tomorrow. Unfortunately if I don’t have them done by tomorrow it will be Wednesday.

## Catch-up Class — Combination of St Patrick’s Day and Wednesday Morning’s Cancelled Lecture

Tuesday 20 March, 13:00 – 14:00 in B212.

## Week 7

We started looking at the inverse Laplace transform after looking at partial fractions.

## Week 8

In our three lectures we will drive into Section 3.4 in the hope that if you so wish to do so, you can complete (or almost complete) Assignment 2 over Easter. After Easter we should be able to return to two tutorials per week.

## Assignment 2

Assignment 2 will have a hand-in date of 17:00 23 April: the Monday of Week 11. Assignment 2 is in the manual, P. 149. Once we get someway into the examples on p.105, you should be able to make a start.

*These starred week numbers are one behind CIT’s week numbers. This is because of the snow.

## Linear Algebra: 20% Test

Takes place Wednesday 21 March, in Week 7* [21 March].

The test will take place from 19:00-20:30 but most students should be able to complete the test in about an hour. It has about 35 Marks worth of questions: five in all (with one very short, and three shortened versions of longer questions).

Anything done in the first five weeks is examinable (see “Independent Learning” below) and it is recommended that you understand what is going on with the summaries of p. 57-59.

The nine questions from p. 60 on are a good revision but not every possible question is listed there.

## Week 6* [14 March]

We started the class with one more example of Cramer’s Rule, and then started pushing into statistics, looking at everything up to and including standard deviation.

In Maple, we did Lab 3, which was really revision for the Linear Algebra Test.

## Week 7* [21 March]

The test is going to begin at 19:00 sharp and run until 20:30. Class will resume at 20:35 sharp. This seems a very short break but the test is designed so that it shouldn’t take much longer than an hour to complete, so almost everyone should have a solid enough break.

At 20:35 we will continue working on statistics by looking at frequency distributions.

## Week 8* Snow Day Catch Up [28 March]

This may or may not be a Maple night (it depend on how far we get in the previous week).

Any students who cannot make this class should email me and request that the class be recorded (I might not be able to record all of the class but most of it.

## VBA Assessment 1 – Results

I would hope to have these with ye by the end of Week 8.

## Written Assessment 1 – Results

I would hope to have these with ye by the end of Week 8

## Week 7

In the first lecture you sat your first written assignment.

In the second lecture we looked more at boundary value problems (in particular the Shooting Method and Goal Seek). We started talking about Finite Differences.

In VBA we looked at Runge-Kutta methods.

*These starred week numbers are one behind CIT’s week numbers. This is because of the snow.

## Linear Algebra: 20% Test

Will now take place Wednesday 21 March, in Week 7* [21 March].

The test will take place from 19:00-20:30 but most students should be able to complete the test in about an hour. It has about 35 Marks worth of questions: five in all (with one very short, and three shortened versions of longer questions).

Anything done in the first five weeks is examinable (see “Independent Learning” below) and it is recommended that you understand what is going on with the summaries of p. 57-59.

The nine questions from p. 60 on are a good revision but not every possible question is listed there. In next week’s Maple you will get a chance to revise these questions.

## Week 5* [7 March]

We saw how linear systems can be written as matrix equations, and (sometimes) solved using matrix inverses. Then we spoke about determinants, and their use in figuring out if homogeneous linear systems have non-zero solutions. Finally we looked at Cramer’s Rule.

## Week 6* [14 March]

We will start the class with one more example of Cramer’s Rule, and then start pushing into statistics.

In Maple, we will do Lab 3, which is really revision for the Linear Algebra Test.

## Week 7* [21 March]

The test is going to begin at 19:00 sharp and run until 20:30. Class will resume at 20:35 sharp. This seems a very short break but the test is designed so that it shouldn’t take much longer than an hour to complete, so almost everyone should have a solid enough break.

At 20:35 we will continue working on statistics.

## Week 8* [28 March/4 April]

This may or may not be a Maple night (it depend on how far we get in the previous week).

It appears that at most one student will miss the class, which isn’t too bad. So now we now go back to the poll to pick between the two nights.

## Week 6

We started looking at “The Engineer’s Transform” — the Laplace Transform. We looked at the first shift theorem, and how the Laplace Transform interacts with differentiation. We started looking at partial fractions.

## Week 7

We will continue looking at partial fractions and the inverse Laplace Transform.

## Assignment 2

Assignment 2 will have a hand-in date of 17:00 23 April: the Monday of Week 11. Assignment 2 is in the manual, P. 149. Once we get someway into the examples on p.105, you should be able to make a start.

## Written Assessment 1

Written Assessment 1 takes place Tuesday 13 March at 09:00 in the usual lecture venue.

Here is a copy of last year’s assessment. This should give you an idea of the length and format but not what questions are coming up. There are far more things I could examine.

Roughly, everything up to p. 57 is examinable. More specifically:

### Maclaurin/Taylor Series

Examples 1 & 2 on p. 17; Q. 1-2 on p.19

### ODEs in Engineering

p.22, Example, Q. 1-4

### Euler Method

p.29, Examples 1-4; p.38, Q. 1-6, 8-9; p.48, Q. 1, 5(a)

### Three Term Taylor Method

p.35, Example; p. 36, Examples 1-2; p.38, Q. 6-7, 10-14; p.48, Q. 3

### Heun’s Method

p.43, Examples 1-2; p.48, Q. 2, 4, 5(b)

### Second Order Differential Equations

p.52, Example; p.54, Example; p. 56, Q. 1-14 (some repetition here).

## VBA Assessment 1

VBA Assessment 1 will take place in Week 6, (6 & 9 March) in your usual lab time. You will not be allowed any resources other than the library of code (p.124) and formulae (p.123 parts 1 and 2) at the end of the assessment (both are provided on the assessment paper). More information in last week’s weekly summary.

“Straight-Line-Graph-Through-The-Origin”

The words of Mr Michael Twomey, physics teacher, in Coláiste an Spioraid Naoimh, I can still hear them.

There were two main reasons to produce this straight-line-graph-through-the-origin:

• to measure some quantity (e.g. acceleration due to gravity, speed of sound, etc.)
• to demonstrate some law of nature (e.g. Newton’s Second Law, Ohm’s Law, etc.)

We were correct to draw this straight-line-graph-through-the origin for measurement, but not always, perhaps, in my opinion, for the demonstration of laws of nature.

The purpose of this piece is to explore this in detail.

## Direct Proportion

Two variables $P$ and $Q$ are in direct proportion when there is some (real number) constant $k$ such that $P=k\cdot Q$.

## Assignment 1

Due to the weather, Assignment 1 now has a hand-in time and date of 17:30 Monday 5 March (Week 6).

## Assignment 2

Assignment 2 will have a hand-in date of 17:00 23 April: the Monday of Week 11. Assignment 2 is in the manual.

## Week 5

We finished our study of the method of undetermined coefficients.

## Week 6

We will start looking at “The Engineer’s Transform” — the Laplace Transform.

## VBA Assessment 1

VBA Assessment 1 will take place in Week 6, (6 & 9 March) in your usual lab time. You will not be allowed any resources other than the library of code (p.124) and formulae (p.123 parts 1 and 2) at the end of the assessment (both are provided on the assessment paper). More information in last week’s weekly summary.

## Written Assessment 1

Written Assessment 1 takes place Tuesday 13 March at 09:00 in the usual lecture venue.

Here is a copy of last year’s assessment. This should give you an idea of the length and format but not what questions are coming up. There are far more things I could examine.

Roughly, everything up to p. 57 is examinable. More specifically:

### Maclaurin/Taylor Series

Examples 1 & 2 on p. 17; Q. 1-2 on p.19

### ODEs in Engineering

p.22, Example, Q. 1-4

### Euler Method

p.29, Examples 1-4; p.38, Q. 1-6, 8-9; p.48, Q. 1, 5(a)

### Three Term Taylor Method

p.35, Example; p. 36, Examples 1-2; p.38, Q. 6-7, 10-14; p.48, Q. 3

### Heun’s Method

p.43, Examples 1-2; p.48, Q. 2, 4, 5(b)

### Second Order Differential Equations

p.52, Example; p.54, Example; p. 56, Q. 1-14 (some repetition here).

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.

## Week 4

We worked with matrix inverses, seeing how the Gauss-Jordan algorithm can be used to calculate the inverse of a $3\times 3$ matrix. We solved a matrix equation.

Here find a corrected Example 2 from p. 39. In class, I made a slip in the third frame. The row operations are the same.

$\displaystyle A^{-1}=\left(\begin{array}{ccc} 1 & 1 & 1 \\ 3 & 5 & 4 \\ 3 & 6 & 5\end{array}\right)$.

We also had our second Maple lab.

## Week 5

We will see how linear systems can be written as matrix equations, and solved using matrix inverses. Then we will talk about determinants, and perhaps push towards the end of Chapter 1.

## Linear Algebra: 20% Test

Will take place Wednesday 14 March, in Week 7.

## Maple Catch Up

If you have missed the first lab you have two options: either download Maple onto your own machine (instructions may be found here) or come into CIT at another time to use Maple.

Go through the missed lab on your own, doing all the exercises in Maple. Save the worksheet and email it to me.