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## 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.

## 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.

## 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.

## Assignment 1

Assignment 1 has a hand-in time and date of 14:30 Friday 2 March (Week 5) and has been given out.

Careful in your “collaboration” — don’t take an explanation, etc. from another
student unless it makes sense to you: otherwise you are not going to get the benefit out of completing this assignment.

## Week 4

We continued our work on Chapter 2 — the method of undetermined coefficients for solving linear odes — by looking at the case of external forces. We had two tutorials.

## Week 5

We will hopefully finish off our work on the method of undetermined coefficients: we will start the second tutorial (Thursday) only when we finish Section 2.4 (what if we know the initial conditions).

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.

## Assignment 1 – Warning

Assignment 1 has a hand-in time and date of 14:30 Friday 2 March (Week 5) and has been given out.

This assessment is worth 15% of your final grade. The corresponding question on the final exam is worth 24.5% of your final grade. This assessment is designed to aid your understanding of this topic and go on to score well in the final exam.

Careful in your “collaboration” — don’t take an explanation, etc. from another
student unless it makes sense to you: otherwise you are not going to get the benefit out of completing this assignment.

## Postponed Lecture

There will be no class this coming Monday, 19 February. This class will instead take place at 13:00 on Tuesday, 20 February: in B212.

## Week 3

We looked at applications to temperature distribution, where the Jacobi Method is used to find approximate solutions to a diagonally dominant linear system. We started work on Chapter 2 — the method of undetermined coefficients for solving linear odes.

In tutorial you worked on applications of linear systems (flow networks and plates).

## Week 4

We will continue our work on Chapter 2 — the method of undetermined coefficients for solving linear odes.

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 2

We finished looking at Gaussian Elimination (including Gaussian Elimination with Partial Pivoting — absolutely necessary if you are rounding.).

If you download Maple (see Student Resources), there is a Maple Tutor that is easy to use and will help you. Open up Maple and go to Tools -> Tutors -> Linear Algebra -> Gaussian Elimination.

We looked at applications to network flows: traffic and pipes.

## Week 3

We will look at applications of linear systems to temperature distribution.

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 1

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.

If you download the software package Maple (see the Student Resources tab at the top of this page), there is a Maple Tutor that is easy to use and will help you. Open up Maple and go to Tools -> Tutors ->Linear Algebra -> Gaussian Elimination.

## Week 2

We will do some more examples in class before giving you some opportunity to practise.

## Assessment 1

Assessment 1 has a hand-in date of Friday 2 March (Week 5). Expect to see the assignment next week.

## Study

Please feel free to ask me questions about the exercises via email or even better on this webpage.

## Student Resources

Quadratics are ubiquitous in mathematics. For the purposes of this piece a quadratic is a real-valued function $q:\mathbb{R}\rightarrow \mathbb{R}$ of the form

$q(x)=ax^2+bx+c$,

where $a,\,b,\,c\in \mathbb{R}$ such that $a\neq 0$. There is a little bit more to be said — particularly about the differences between a quadratic and a quadratic function but for those this piece is addressed to (third level: non-maths; all second level), the distinction is unimportant.

## Geometry

The basic object we study is the square function, $s:\mathbb{R}\rightarrow \mathbb{R}$, $x\mapsto x^2$:

All quadratics look similar to $x^2$. If $a>0$ then the quadratic has this $\bigcup$ geometry. Otherwise it looks like $y=-x^2$ and has $\bigcap$ geometry

The geometry dictates that quadratics can have either zero, one or two real roots. A root of a function is an input $x$ such that $f(x)=0$. As the graph of a function is of the form $y=f(x)$, roots are such that $y=f(x)=0\Rightarrow y=0$, that is where the graph cuts the $x$-axis. With the geometry of quadratics they can cut the $x$-axis no times, once (like $s(x)=x^2$), or twice.

There are a number of ways of explaining why you cannot divide by zero. Here are my two favourites.

## Any Set of Numbers Collapses to a Single Number

How old are you? Zero years old.

How tall are you? Zero metres old.

How many teeth do you have? Zero.

How many Superbowls has Tom Brady won? Zero

Yep, if you allow division by zero you only end up with one number to measure everything with.

## Assignment 2

Assignment 2 has a hand-in date of this 24 April and a hand-in time of 17:30. Work handed in late will be assigned a mark of zero so hand in what you have on time. You can hand in your work in class or drop it to A283.

Befitting of the second semester of the award year of a major qualification, this is a difficult assignment. Some of the questions will stretch you more than the work you have done in tutorials. If you are having difficulties completing this assignment over Easter feel free to email me looking for help.

If you can handle what this assignment throws at you not only will you be in a good position for your final exam you will also be in a good position DSE3.

Also, you are in the award year of a major qualification: the Easter break isn’t a break.

## Student Feedback

If you would like to submit anonymous feedback on this module/lecturer, you may take the do so here. This link will be open until May 11.

## Week 10

We looked at systems of differential equations.

## Weeks 11 & 12

We will look at double and triple integrals.

## Week 13

We will go through last year’s exam on the board and then I will answer your questions if there are any. If there are none I will help one-to-one.