You are currently browsing the category archive for the ‘MS 2001’ category.

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

## Projects

These are finally corrected. I would like to apologise for the inexplicable delay… you are identified by the last five digits of your student number. Remarks below.

 S/N Mark Ex 12.5 27898 12.5 29579 12.5 89138 12.5 35809 12 00988 12 05441 12 72936 11.5 31148 11 59663 11 89362 11 19801 10.5 76939 10 55503 10 64923 10 50316 10 56576 9.5 01642 9.5 81431 9.5 28745 9.5 25441 9 11938 9 93481 9 40198 9 37211 9 28575 8.5 30609 8 09341 8 98786 8 04996 7.5 21361 7.5 21967 7 29768 7 00633 7 59593 6.5 84181 6 35726 6 32338 5.5 07743 5.5 30948 5.5 74522 4.5 47692 4.5 93528 4 28475 4 59528 3.5 15585 3.5 71579 3 09658 3 47796 5 64301 5

### Remarks

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

## Lectures

We finished off the sections on the closed interval method, the first derivative test and the second derivative test. This means that we can find the

• absolute maxima/minima of continuous functions defined on closed intervals
• local maxima/ minima of continuous functions defined on the entire real line
• local maxima/ minima of some differentiable functions defined on the entire real line

This means that we have enough theory to do the applied optimisation problems. However as we have only two lectures left and I don’t want to rush anything we will not be doing these in class. These applied optimisation problems occur when we have a cost function of several variables which we want to maximise or minimise.

$C=C(x_1,x_2,\dots,x_n).$

We have only studied functions of a single variable in MS2001. However if there are relationships/constraints between the variables:

$f_i(x_1,x_2,\dots,x_n)=0$ for $i=1,2,\dots,N$,

then we may be able to eliminate all but one of the variables and write

$C=C(x)$ only.

Then we can use the methods above to find the extrema of $y=C(x)$.

As this material will not be covered in class by examples, the exam question will either ask to find the maximum of a function of  a single variable (Autumn ’12 $\ell(x)=\sqrt{a^2+x^2}$ with $a$ a constant) or the relationship between the variables will be obvious (Example on p.115, $d(x,y)=\sqrt{(x-3)^2+y^2}$ with $y=x^2$).

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

## Lectures

We did implicit differentiation and have up to the Closed Interval Method done from Chapter 4.

## Tutorials

Remember you can ask whatever you want in tutorials. If you have questions about the test or past exam papers work away.

### Tutorial 9 Question Bank

Questions 14 – 15 from Exercise Sheet 3. Questions 1 – 2 from Exercise Sheet 4 (When asked to find the critical points of a function defined on the entire real line (rather than just on a closed interval $[a,b]$), the ‘endpoints’, $\pm\infty$ are not considered critical points.).

Question 4: 1-3, 4(a) from MS2001: Problems (after page 102 in the notes).

Questions 5, 6, 13 – 18, 28, 33  from the Additional but Harder Exercises for Definitions II (two after page 108 in the notes).

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

## Lectures

We have all but finished with the Mean Value Theorem. Six more lectures left covering question 3(b) and Q. 5 on the final exam.

## Tutorials

Remember you can ask whatever you want in tutorials. If you have questions about the test or past exam papers work away.

### Tutorial 8 Question Bank

Questions 4, 21, 30 and 31 are very good questions from the Additional but Harder Exercises for Definitions II (two after page 108 in the notes) to look at for Rolle’s Theorem and the Mean Value Theorem.

Questions 6 and 10 – 12 from Exercise Sheet 3.

Also Questions 19, 32 and 36  from the Additional but Harder Exercises for Definitions II (two after page 108 in the notes).

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

## Homework

Please find the Homework. Before you open it don’t be too alarmed: you only have to do ONE of the NINE options. All of the options are about differential calculus:

1. Nowhere-Continuous Functions
2. Intermediate Value Theorem
3. Fixing Nasty Functions and Making them Nice
4. Summarise Limits & Continuity
5. “Leaving Cert Questions”
6. L’Hopital’s Rule
7. Linear Algebra
8. Summarise Differentiation
9. Extrema of Functions of Several Variables with an Application to Statistics — contains a typo. Q.9 (a) should read “Show that (1, 1) and (−1,- 1) are local minima…” not “Show that (1, 1) and (−1, 1) are local minima…”. Also you can find the partial derivatives $\frac{\partial S}{\partial m}$ and $\frac{\partial S}{\partial c}$ without multiplying out $S(m,c)$

I am not going to pretend that this is an easy assignment, but I will say that clear and logical thinking will reveal that the solutions and answers aren’t ridiculously difficult: a keen understanding of the principles of differential calculus should see you through.

Roughly, I have gone with less thinking & more writing or more thinking & less writing but half the battle here is picking an option that you think you can do well.

The final date for submission is 01 February 2013 and you can hand up early if you want. You will be submitting to the big box at the School of Mathematical Science. If I were you I would aim to get it done and dusted early.

Note that you are will be free to collaborate with each other and use references but this must be indicated on your hand-up in a declaration. Evidence of copying or plagiarism will result in divided marks or no marks respectively. You will not receive diminished marks for declared collaboration or referencing although I demand originality of presentation. If you have a problem interpreting any question feel free to approach me, comment on the webpage or email.

Ensure to put your name, student number, module code (MS 2001), and your declaration on your homework.

## Lectures

We have finished up to but not including Section 3.2

## Tutorials

Remember you can ask whatever you want in tutorials. If you have questions about the test or past exam papers work away.

### Tutorial 7 Question Bank

Questions 3, 5, 7, 8, 13, 16, 17 from Exercise Sheet 3.

Question 3 from MS2001: Problems (after page 102 in the notes)

Questions 14, 20, 29, 35  from the Additional but Harder Exercises for Definitions II (two after page 108 in the notes).

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

## Question 3 Solutions

May be found here.

## Lectures

We have finished up to and including Proposition 3.1.5.

Pending…

## Tutorials

Remember you can ask whatever you want in tutorials. If you have questions about the test or past exam papers work away.

### Tutorial 6 Question Bank

Questions 1, 2, 3 (i), (iii), 4, 7 (i), 8 (a) (i), (ii), 9, 13 (i) from Exercise Sheet 3.

Questions 35  from the Additional but Harder Exercises for Definitions II (two after page 108 in the notes).

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

## Test Results

Test Results

First of all results are down the bottom. You are identified by the last five digits of your student number. Included are some average scores.

If you would like to see your paper or have it discussed please email me.

Students with no score were either absent in which case they score zero — or certified absent in which case their marks carry forward to the summer exam.

Solutions and Remarks

Friday maybe…

If you scored above 70 well done; keep it up. If you scored between 40 and 70 you need to improve. If you scored below or near 40 take this as a wake up call.

 Student No Mark % 35809 12.5 100 59593 12.5 100 50316 12.5 100 29579 12.5 100 89138 12.5 100 56576 12 96 19801 11.5 92 55503 11.5 92 89362 11.5 92 27898 11 88 98786 11 88 81431 11 88 05441 11 88 09341 10 80 64923 10 80 32338 10 80 93528 10 80 76939 9.5 76 11938 9.5 76 35726 9.5 76 74522 9.5 76 28756 9.5 76 59528 9.5 76 47796 9 72 97812 9 72 86131 9 72 64301 9 72 25441 8.5 68 93481 8.5 68 12256 8 64 59663 8 64 01642 8 64 Median 8 64 30948 8 64 Mean 7.5 60.26 04996 7.5 60 29768 7.5 60 40198 7.5 60 15585 7.5 60 19076 7.5 60 21967 7 56 72936 7 56 21361 6.5 52 00988 6.5 52 54513 6.5 52 07743 6.5 52 59268 6 48 37211 6 48 28585 6 48 31148 5 40 07723 5 40 47692 4 32 09658 3.5 28 59767 3 24 28475 2.5 20 38068 2 16 30609 1 8 84181 1 8 40259 1 8 01947 1 8 00633 abs 0 64879 abs 0 50938 abs 0

## Lectures

We have finished the second chapter and will begin Chapter 3: Differentiability next week.

## Homework

I am officially trying to draft your homework as soon as possible. It is probably going to have a due date in January but I haven’t made a concrete decision about it yet…

## Tutorials

Remember you can ask whatever you want in tutorials. If you have questions about the test or past exam papers work away.

### Tutorial 5 Question Bank

Questions 6 (iv), (v), (vii), 8, 9  from Exercise Sheet 2 — but don’t worry about removable and essential discontinuities (after page 62 in the notes).

Question 1 from MS2001: Problems (after page 108 in the notes)

Questions 1, 2, 3, 10, 11, 12, 13, 27  from the Additional but Harder Exercises for Definitions II (two after page 108 in the notes).

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

## Test

The test will take place at 3 pm in WGB G 05 next Friday 2 November in Week 6.

I would’ve intended that everything up to and including section 2.2 is examinable for the test.

You can find the tests I set for the last two years after Exercise Sheet 1 — which is itself after page 49. Also there is a sample from last year here.

As we will not have covered continuity, we will not be able to do the questions two as they are phrased. However we have covered limits.

I will make some brief remarks on these tests now.

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

## Test

The test will take place at 3 pm on Friday 2 November in Week 6.

I would’ve intended that everything up to and including section 2.3 would be examinable for the test. However it looks like we will not finish section 2.3 next week so Section 2.3: Continuity will not be on the test.

You can find the tests I set for the last two years after Exercise Sheet 1 — which is itself after page 49. Also there is a sample from last year here.

As we will not have covered continuity, we will not be able to do the questions two as they are phrased. However we have covered limits.

I will make some brief remarks on these tests now.

I am emailing a link of this to everyone on the class list every Friday afternoon. 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.ie and I will add you to the mailing list.

## Lectures

We are just about finished with Chapter 1.

## Tutorials

I don’t think what I was going on about last week is going to work is it? We’ll play it by ear now.

I will happily answer questions from past papers also but I won’t but them in the question bank.

## Tutorial 2 Question Bank

Questions 4, and 6 – 8 from Exercise Sheet 1 (after page 59 in the notes).

Questions 1 – 3 from MS2001: Exercises (before page 63 in the notes)

Questions 17 – 22 and 24 – 26 from the Additional but Harder Exercises for Definitions I (just before page 60 in the notes).

## Tutorial 1 Question Bank

Questions 1, 2 and 5 from Exercise Sheet 1 (after page 59 in the notes).

Questions 1 to 16 from the Additional but Harder Exercises for Definitions I (just before page 60 in the notes).