MATH6000: Week 1

September 21, 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.

Notes

As of 21 September: MATH6000.

Also an E-Book: Engineering Mathematics by John Bird.

Exercise

Tutorials start in Week 2. The exercises are found in your notes, the starred are probably the most important in terms of the tests. All the exercises have been collate here.

Timetable

My best understanding is that your timetables are still changing. I will see ye in class to give the latest information that I have.

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MATH6015: Week 1

September 21, 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.

Notes

So far we have covered the revision of functions and motivation.

Timetable

My best understanding is that your timetable has been changed. You will now see me

Monday at 4 in B260

Tuesday at 9 in B262

Thursday at 11 in B188

Friday at 9 in PF45

This is still not finalised but is the state of play as we speak.

Continuous Assessment

There has been a late changes to the continuous assessment and coursework breakdown. This can be seen here in the Module Descriptor.

Rather than a 20% test in week 6 there will now be two 15% tests: one in Week 5 and one in Week 10. I hope to give you two week’s notice of each of these and also provide sample tests.

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MS3011: Summer 2012 Solutions

July 12, 2012 in MS 3011 | Leave a comment

Please find pdf files containing solutions to the summer exam here, here, here, here, here, here and here.

Due to not having Adobe Acrobat in the lab and not being very good at using the scanner these files are mixed up and by and large comprise the bits and pieces of pages.

MS2002: Summer 2012 Solutions

July 12, 2012 in MS 2002 | Leave a comment

Please find pdf files containing solutions to the summer exam here and here.

Due to not having Adobe Acrobat in the lab and not being very good at using the scanner these files are mixed up and by and large comprise the odd pages and the even pages.

MS2001: Summer 2012 Solutions

July 12, 2012 in MS 2001 | Leave a comment

Please find pdf files containing solutions to the summer exam here and here.

Due to not having Adobe Acrobat in the lab and not being very good at using the scanner these files are mixed up and by and large comprise the odd pages and the even pages.

MS3011: Homework Results and Final CA Grades

May 22, 2012 in MS 3011 | Leave a comment

First of all results are down the bottom. The projects were all marked out of 75 and the second column is the CA mark you are carrying with your summer exam. You are identified by the last five digits of your student number. At the bottom there are some average scores.

Students with no score either handed in no project or handed up late.

The *S/N mark denotes that you were certified absent from the Test. Your exam will now be worth 87.5.

If you would like to discuss your project please email me.

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MS2002: Project Results and Final CA Grades

May 11, 2012 in MS 2002 | Leave a comment

First of all results are down the bottom. The projects were all marked out of 75 and the second column is the CA mark you are carrying with Wednesday’s exam. You are identified by the last five digits of your student number. At the bottom there are some average scores.

Students with no score either handed in no project or handed up late.

The *S/N mark denotes that you were certified absent from Test 1. Your exam will now be worth 87.5.

If you would like to discuss your project please email me. A lot of people made very fundamental errors and this is where most marks were lost.

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MS 3011: Week 9

March 4, 2012 in MS 3011 | 12 comments

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 jippo@campus.ie and I will add you to the mailing list.

This Week

We started the section complex dynamical systems. We introduced the complex numbers by looking at the following equations:

x+5=10.

x+10=5.

5x=6.

x^2=2.

x^2=-1.

We said that the ‘need’ for complex numbers is analogous to the fact that we can solve the first equation using natural numbers \mathbb{N} but we require

  • negative integers to solve the second equation (\mathbb{Z})
  • fractions to solve the third equation (\mathbb{Q})
  • real numbers to solve the third equation (\mathbb{R})
  • and finally, complex numbers to solve the fourth equation (\mathbb{C})

MS 2002: Test Results

March 4, 2012 in MS 2002 | Leave a comment

First of all results are down the bottom. You are identified by the last five digits of your student number. The scores are itemized as you can see. At the bottom there 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.

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MS 2002: Week 9

March 2, 2012 in MS 2002 | Leave a comment

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 jippo@campus.ie and I will add you to the mailing list.

This Week

We finished the chapter on area and volume and we have began the chapter on differential equations.

In tutorials we looked at p. 59 Q. 1(a), 2(a)(c)(f), 3(c) and p.64 Q. 4(e)(f).

Mistakes in Notes!!

  1. The formula for the volume of a doughnut/torus on p.97 is correct — there is a \pi^2 term.
  2. Autumn 2011 Q.2(b)(ii) P. 99 My geometric intuition led me astray here I am afraid. The equation that governs the rotation about the x-axis (and the generalisation to rotations about y=d) use a summation of cylinders and the “big volume” – “hole” idea works perfectly. However, when rotating around the y-axis things are different and we derived our formula using cylindrical shells (animation). This means that the “big volume” – “hole” perspective is not going to work. What is actually happening in this question is we are generating a cylindrical shell as per the animation above by rotating the below strip about the y-axis.

In this case the height of the strip (corresponding to height of the red plus the yellow) is given by x-(x^2-2x). This is directly analogous to the situation where we find the area between two curves as the integral of “top curve minus bottom” curve. Therefore I should have never put the - in front of

\displaystyle V=\int_0^32\pi x[x-(x^2-2x)]\,dx,

and the answer is \frac{27}{2}\pi. Note that we shouldn’t blindly change the -\frac{27}{2}\pi that we got in class. If we use our formulae correctly then we shouldn’t get meaningless answers. In fact this question serves a timely reminder that to use a “formula” with total aptitude you should probably know how to derive it — this suggests the extent and limits of its application.

Thus, if we ever want to find the volume generated by rotating a region B, lying in the right-half plane, (bounded by curves y=f(x) and y=g(x)), about the y-axis, we should use:

\displaystyle V=\int_a^b 2\pi x[\text{``top curve''- ``bottom curve''}]\,dx.

Exercise from Notes

Evaluate the integrals in Summer 2011 Q. 2(c)

Test Results

Sunday all going well.