## Test 2

Test 2, worth 15% and based on Chapter 3, will now take place Week 12, 30 April. There is a sample test in the notes and the test will be based on Chapter 3 only.

## Homework Exercises

If you do any of the suggested exercises you can give them to me for correction. Please feel free to ask me questions about the exercises via email or even better on this webpage.

I recommend strongly that everyone completes P.102, Q.1.

After that you can look at:

- P.136, Q.1-3
- P. 143, Q. 1-4
- P. 125, Q. 1-4, P.172, Q.1
- P. 117, Q. 1-4
- P.112, Q. 1-5
- Sample Test 2, P.145

If you want to do more again, look at P.113, Q.6-9, P. 118, Q. 5-6, P. 125, Q.5. There is a Weekly Summary for the Chapter 3 Material on P.144.

If you read on there is some information below about solutions to these exercises.

## Week 10

For those who were able to make it we had some tutorial time from 18:00-19:00 for parametric, implicit, and related rates differentiation. If you are really interested in understanding how does a curve have an equation, see here.

In class we looked at partial differentiation and error analysis. For those who could not make it, here is video of the partial differentiation material and here are the slides from the error analysis (the video died shortly after we started error analysis).

We only started a revision of Antidifferentiation to start Chapter 4 on (Further) Integration. I have this section completed here.

## Week 11

We will have some tutorial time from 18:00-19:00 for further differentiation (i.e. for Test 2, after Easter).

We are under pressure for time but I have made the decision that we will be better off completing our review of antidifferentiation before starting Chapter 4 proper. This might put us under time pressure later on but I believe it is the correct thing to do.

We will look at Integration by Parts, completing the square, and work.

## Week 12

We will have some tutorial time from 18:00-19:00 for further differentiation.

We will have Test 2 from 19:00-20:05.

Then we will look at centroids and centres of gravity.

## Week 13

We will look the Winter 2018 paper at the back of your manual.

## Homework Solutions?

A couple of students approached me last night inquiring about solutions for exercises. Firstly I want to apologise to the students: I didn’t really give ye a proper explanation of why I am not going to be providing solutions to exercises.

A bit of background is that when students are working on questions on an evening, while they can email me questions, they are not going to get a response until the next morning. In reality sometimes I do answer emails promptly and one thing I should have said to the students is… try… try send an email. I am not getting many emails nor handed up work and it is up to students to take that opportunity.

Well anyway, the students were wondering could I provide solutions to the exercises in the notes.

What I didn’t really explain to the students is as follows: basically there are two approaches to learning – shallow and deep. I am actually going to meet my HoD today about the fact that it is my opinion that the cramming of so many topics into your two maths modules is almost forcing you to take a shallow approach.

Usually a shallow approach to learning in mathematics would consist of learning from examples: basically doing loads of questions out and “getting the method”.

My big problem with this approach to learning is that it doesn’t persist: this kind of learning might get you through an exam but the knowledge and skills you pick up using this type of learning is going to leave your head as fast as it enters.

What is far more beneficial is a deep approach to learning.

Usually a deep approach to learning in mathematics is driven largely by “understanding” rather than what might be called “method”. A deep approach will involve taking from lectures an understanding, however rough, of what is going on, and taking that understanding and using it to attack exercises. When you get answers correct, your understanding is probably sound, but when you get answers wrong, or don’t know where to start, your understanding isn’t what it needs to be. At this point you look back at the notes and yes, perhaps examples, to see where your understanding is lacking. Hopefully you pick up the understanding that is missing and in my opinion this is what learning is.

Having said all that, I said beforehand more-or-less than a deep approach to MATH6040 is difficult because you are under time pressure and there are so many topics. Therefore you are kind of forced into a shallow approach: I still think a deep approach is better but I appreciate that you are in a short term thinking situation where your aim to do well in exams.

This means there must be some kind of leeway. Where this leeway exists is in the fact that the notes contain loads of worked examples — the examples we complete in class as well as worked examples in the notes (see below).

Taking Chapter 3, into the five sections:

- parametric differentiation: 4 examples in lectures, one worked example with comments (p. 111)
- related rates: 4 examples in lectures, one worked example with comments (p. 117)
- implicit differentiation: 5 examples in lectures, one worked example with comments (p. 124)
- partial differentiation: 5 examples in lectures, one worked example with comments (p. 136), selected solutions to exercises are also included
- error analysis: 3 examples in lectures, two worked example with comments (p. 141)

If a student doesn’t want to try an exercise without a solution I would invite them to try examples we did in class or worked examples without looking at the solutions.

But my advice would be to struggle on with the exercises… and do email questions.

## CIT Mathematics Exam Papers

These are not always found in your programme selection — most of the time you will have to look here.

## Student Resources

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

## 2 comments

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April 7, 2019 at 8:20 am

StudentHi J.P.,

I have some questions scanned for correction. The ones with ? I’m just unsure whether they’re correct and ones highlighted I had an issue somewhere with them and either couldn’t answer or not sure if procedure is right or not. The first one on P. 113 highlighted Q.4 I figured out after.

Thanks.

April 7, 2019 at 8:36 am

J.P. McCarthyStudent,

Please ask me about some more of these in the tutorial time this Tuesday or the Tuesday after Easter. There are too many highlighted parts to answer and when you went on to get the correct answer I largely ignored those questions.

Some comments only:

Q. 8, p.113: using you calculator you should get , which is in radians. Use in subsequent calculations rather than the decimal approximation. Also, when inputting consider putting in (watch our for which gives . You made this error in getting -1.95).

You won’t be asked to calculate a second derivative in partial differentiation — just that if you have a graph you can tell whether the second derivative is positive or negative at the point in question.

Q. 4, p.125 you had all but correct. Careful to write not as you have. Anyway, you have, correctly, but note that (see question) and so .

Q. 5 (d), P.125 is correct. The answer only looks different:

Q. 6 (e), P.125 is correct because .

The full solutions to Q.1, p.136 is on p.137.

Q.2, P.136 you are very close. You have

.

Which is equal to

.

Regards,

J.P..