You are currently browsing the category archive for the ‘MATH7021’ category.

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:

graph1

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.

Read the rest of this entry »

Advertisements

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.

Read the rest of this entry »

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.

Read the rest of this entry »

Assignment 2

Assignment 2 will have a hand-in date of Monday 24 April. There is extra help to set you up, Wednesday 5 April, 16:00 – 17:30 in B188.

Week 9

Ye solved some differential equations using Laplace Transforms.

Week 10

We will work on systems of ordinary differential equations.

Read the rest of this entry »

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 2

Assignment 2 will have a hand-in date of 24 April. There is extra help to set you up, Wednesday 5 April, 16:00 – 17:30 in B188.

Week 8

We solved some differential equations using Laplace Transforms.

Week 9

I will say a few things about damped harmonic oscillators on Monday and give you some more time to work on exercises.

Read the rest of this entry »

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 — Results

I will have these for you by the Monday of Week 8, 20 March.

Assignment 2

Assignment 2 will have a hand-in date of 24 April: the Monday of Week 11. I will give it to ye in Week 8.

Catch-up Class — Help for Assignment 2

Wednesday 5 April, 16:00 – 17:30 in B188.

Week 7

We started looking at the inverse Laplace transform and so partial fractions.

Week 8

We might solve some differential equations using Laplace Transforms.

Read the rest of this entry »

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 — Results

I will have these for you by the Monday of Week 8, 20 March.

Assignment 2

Assignment 2 will have a hand-in date of 24 April: the Monday of Week 11. I will give it to ye in Week 8.

Week 6

We started looking at “The Engineer’s Transform” — the Laplace Transform. We missed two lectures and we will look to catch up on these over the next few weeks.

Week 7

We will start looking at the inverse Laplace transform and so partial fractions.

Read the rest of this entry »

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

Hand in is tomorrow, Friday 16:30 (I have extended this by two hours), Friday 3 March. I am not sure how soon I will have these corrected.

Assignment 2

Assignment 2 will have a hand-in date of 24 April: the Monday of Week 11. I have the assignment ready but ye can’t do any of the questions yet.

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.

Read the rest of this entry »

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.

Assessment 1

The hand in date is 14:00 Friday 3 March. If you have the assignment completed on Thursday hand it to me in class otherwise drop it in A283. Work submitted after 14:00 on Friday 3 March will be assigned a mark of zero. Hand up whatever you have on time.

Week 4

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

Week 5

We will finish working on Chapter 2.

Read the rest of this entry »

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 3

You worked on problems with partial pivoting and application and we looked at applications to temperature distribution, where the Jacobi Method is used to find approximate solutions to a diagonally dominant linear system

Week 4

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

Read the rest of this entry »

%d bloggers like this: