## Student Feedback

If you would like to submit anonymous feedback on this module/lecturer, you may do so here. This link will be open until Friday May 11 2018.

## Week 12

On Monday we finished the module by looking at triple integrals.

The Wednesday 09:00 lecture will be a tutorial. In this class and your usual tutorial we will look at the P.182, P. 192, P. 163, & P.116 exercises. If these are completed you will be recommended to revise either by trying Chapter 1 & 2 exercises or perhaps by looking at the Summer 2017 paper.

As next Monday is a bank holiday, we will begin the Summer 2017 Paper (in your notes) revision on Thursday.

## Week 13

In the Wednesday 09:00 lecture we will continue working on the Summer 2017 Paper and hopefully finish it before the end of the Thursday 10:00 lecture.

If we finish the Summer 2017 paper early, any extra time (probably just Thursday but maybe Wednesday if we go fast) will be dedicated to one-to-one help.

Wednesday’s tutorial will go ahead as normal with one-to-one help.

## Study

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

## Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..

## 4 comments

Comments feed for this article

May 9, 2018 at 12:30 pm

StudentI’m doing question 2, 2017 in the past exam and I don’t know if the answer is correct, could please check it. I send a copy of my solution.

May 9, 2018 at 1:59 pm

J.P. McCarthyI’m afraid your solution is incorrect in many ways.

Looking at the auxiliary equation

is correct. However the factors are

.

This gives a homogeneous solution:

.

Now we look for a particular solution. We trial . This has first and second derivatives and . Force this into the differential equation

.

To satisfy the differential equation this must equal :

, and so we have a particular solution

.

So that the general solution is

.

Now we need to find and such that the initial conditions are satisfied. I will leave this to you.

Regards,

J.P.

May 10, 2018 at 12:05 pm

StudentHow do you spot that .

Is there a long way of doing this out? I won’t get this in the exam if something like this comes up. Do you just have to know that changes to and ?

May 10, 2018 at 12:23 pm

J.P. McCarthyThere are quite a number of ways of seeing this.

It is probably worth pointing out a different problem. Suppose you have

,

and you want to send this back. You look in the table and see that

but isn’t a square… or is it? Any positive number can be written as a square via , and so,

.

This is how you could spot that as .

OK, I have four ways of getting .

1. First of all, just by noticing that it is a difference of squares. We have

,

and indeed any such factor can be factored like this using the above trick:

.

You asked about other ways.

2. The other way is via the Factor Theorem:

a root a factor,

therefore we look for the roots of i.e. we solve it equal to zero:

.

Therefore we have roots and and so factors and :

.

3. The same except that at we use the ‘-b’ formula with :

,

and the rest follows similarly.

4. Pragmatically, you have but the answer has . Multiply this out:

,

so they are equal.

Regards,

J.P.