MATH6015: Week 13

December 12, 2012 in MATH6015 | 2 comments

Test 2 Solutions

Please find the test 2 solutions and marking scheme here.

Exam Layout

Answer Q.1 [40 Marks] and two out of Q. 2, 3, 4 [30 marks each].

Q. 1 — 8 short questions each worth 5 marks each

Q. 2 — Differentiation with applications

Q. 3 — Integration with applications

Q.4 — Applications of differentiation and integration

MATH7021: Week 13

December 10, 2012 in MATH7021 | 7 comments

Exam Layout

Answer four questions: each worth the same marks.

1. Multiple Topics Question

(a) Interpolation (b) Linear Algebra (c) Laplace Methods

2. Interpolation

Finite Difference Methods, Least Squares, Lagrangian Interpolation

3. Linear Algebra

Gaussian Elimination with and without partial pivoting, Cramer’s Rule, Jacobi’s Method, Gauss-Siedel Method

4. Laplace Methods

Three differential equations

5.  Multiple Integration

line integrals, double integrals with applications including second moment of area, triple integrals.

MATH6015: Week 12

December 8, 2012 in MATH6015 | Leave a comment

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.

Week 13

I will run tutorial reviews in the usual lecture venues on

  • Monday 10 December at 16:00*,
  • Tuesday 11 December at 09:00,
  • Thursday 11:00 and
  • Friday 09:00.

*I had said in class that I would not do Monday but I’ve had a change of heart. Please email me if this is clashing with some assessment or other. Also please spread the word on Monday afternoon that I will hold this tutorial.

The different things I can do are:

  1. Talk about exam layout
  2. Answer questions
  3. Do an exam paper
  4. Help one-to-one

I can give the exam layout here:

Answer Q.1 [40 Marks] and two out of Q. 2, 3, 4 [30 marks each].

Q. 1 — 8 short questions each worth 5 marks each

Q. 2 — Differentiation with applications

Q. 3 — Integration with applications

Q.4 — Applications of differentiation and integration

I would prefer to answer questions on the board from people until there are no more.

If there are no questions I will start going through Winter 2010 — which I will have printed out for ye.

If we finish this (doubtful), I will start helping one-to-one.

Test 2 Results

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MATH7021: Week 12

December 7, 2012 in MATH7021 | Leave a comment

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.

Week 13

We will have a lecture/tutorial on Tuesday 11 December from 18:00. We have to finish off multiple integration. I hope to do this in one hour. We will decide as a group when to have our break.

The different things I can do for the tutorial:

  1. Talk about exam layout
  2. Answer questions
  3. Do an exam paper
  4. Help one-to-one

I can give the exam layout here — which is more streamlined than other years:

Answer four questions: each worth the same marks.

1. Multiple Topics Question

(a) Interpolation (b) Linear Algebra (c) Laplace Methods

2. Interpolation

Finite Difference Methods, Least Squares, Lagrangian Interpolation

3. Linear Algebra

Gaussian Elimination with and without partial pivoting, Cramer’s Rule, Jacobi’s Method, Gauss-Siedel Method

4. Laplace Methods

Three differential equations

5.  Multiple Integration

line integrals, double integrals with applications including second moment of area, triple integrals.

I would prefer to answer questions on the board from people until there are no more.

If there are no questions I will start going through Summer 2010 — which I will have printed out for ye.

If we finish this (doubtful), I will start helping one-to-one.

Test 2 Results

You are identified by the last four digits of your student number:

S/N Mark
1496 100
3154 100
1895 98
9331 98
2191 95
9904 90
0107 88
1400 83
8477 80
9902 75
0499 75
1498 73
Median 71.5
5335 70
Mean 69.42
9393 68
9903 68
8931 63
2113 60
7990 55
0756 53
0843 38
1550 35
2296 35
1494 33
1495 33

MS2001: Week 11

December 7, 2012 in MS 2001 | Leave a comment

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).

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MATH6000: Week 12

December 4, 2012 in MATH6000 | Leave a comment

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.

Week 13

Tutorials will be held in the usual lecture venues for:

Applied Biosciences: Monday 10 December at 13:00, Tuesday 11 December at 11:00, Wednesday 12 December at 15:00.

Common Entry Science: Tuesday 11 December at 15:00.

Computing: Tuesday 11 December at 10:00; Wednesday 12 December at 14:00

Assessment 5

Wednesday 12 December in Week 13. Coordinate geometry and graphs are examinable. Consult Blackboard for the latest and definitive information on assessments.

Please find some examples here.

Assessment 4 Results

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MATH7021: Week 11

December 4, 2012 in MATH7021 | Leave a comment

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 2 Results

Hopefully this week.

Schedule — Recently updated

Thursday 6 December 20:00 – 22:00: Finish double integrals and start Triple integrals

Tuesday 11 December 18:00 – 22:00: Finish off multiple integration; Exam Format Review Lecture; Tutorial; etc. Will make a plan on Friday.

Integral

In class we found the anti-derivative \int\cos^2x\sin x\,dx by using the substitution u=\cos x. Here we present an alternative method that manipulates the integrand instead.

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MATH6015: Week 11

December 4, 2012 in MATH6015 | Leave a comment

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 2 Results

Hopefully I should have these by Friday.

Additional Tutorial

An additional tutorial for MATH6015 has been arranged for today Tuesdays 17:00 – 18:00 in PF45. All may attend.

Lectures

We finished off the questions on volumes and work. We continue our work on the mean value of a function and the root-mean-square value of a function. The only topic left is ordinary differential equations.

Week 13

I will run tutorial reviews in the usual lecture venues on Tuesday 11 December at 09:00, Thursday 11:00 and Friday 09:00.

MATH6000: Week 11

December 4, 2012 in MATH6000 | Leave a comment

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.

Week 13

Tutorials will be held in the usual lecture venues for:

Applied Biosciences: Monday 10 December at 13:00, Tuesday 11 December at 11:00, Wednesday 12 December at 15:00.

Common Entry Science: Tuesday 11 December at 15:00.

Computing: Tuesday 11 December at 10:00; Wednesday 12 December at 14:00

Assessment 5

Wednesday 12 December in Week 13. Coordinate geometry and graphs are examinable. Consult Blackboard for the latest and definitive information on assessments.

Assessment 4 Results

Should be released at the end of this week.

Tutorials

You will get exercises on graphing in the notes today.

MS2001: Week 10

December 4, 2012 in MS 2001 | Leave a comment

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).

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