Category Archive

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 12

In Week 12 we looked at how to find the centroid of a plane area and the volume and centre of gravity of a solid of revolution.

Week 13

We will hold review tutorials at the usual lecture times in the usual lecture venues. There will be no review tutorials during the usual tutorial times.

First off, the layout of your exam will be exactly as per Winter 12.

I will field any questions ye might have at this time and if there are no more questions we will do the Autumn 2012 paper.

If we finish this paper I will help ye one-to-one.

Notes

The final set of MATH6040 lecture notes. You might find this E-book useful.

Math.Stack Exchange

If you find yourself stuck and for some reason feel unable to ask me the question you could do worse than go to the excellent site math.stackexchange.com. If you are nice and polite, and show due deference to these principles you will find that your questions are answered promptly. For example this question on the volume of a doughnut.

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.

BioEng Tutorial

Ye can attend the BIS tutorial tomorrow Tuesday 30 April, at 11:00 in F1.3 instead.

Week 11

In Week 11 we finished our work with the inverse trigonometric functions and looked at applications of integration to work.

Week 12

In Week 12 we look at how to find the centroid of a plane area and the volume and centre of gravity of a solid of revolution.

Week 13

We will hold review tutorials at the usual lecture times in the usual lecture venues. There will be no review tutorials during the usual tutorial times.

First off, the layout of your exam will be exactly as per Winter 12.

I will field any questions ye might have at this time and if there are no more questions we will do the Autumn 2012 paper.

If we finish this paper I will help ye one-to-one.

Test 2 Results

You are identified by the last five digits of your student number. T1 refers to Test 1, T2 refers to Test 2. CA/30 refers to your Continuous Assessment Mark out 0f 30. Finally the last column describes the percent you need on your final exam to pass. The final exam is worth 70/100.

Notes

A relatively recent set of MATH6040 lecture notes. You might find this E-book useful.

Math.Stack Exchange

If you find yourself stuck and for some reason feel unable to ask me the question you could do worse than go to the excellent site math.stackexchange.com. If you are nice and polite, and show due deference to these principles you will find that your questions are answered promptly. For example this discussion of some illuminating integrals.

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.

Friday BioEng Tutorial

I will not be here Friday 26 April. Ye can attend the BIS tutorial on Tuesday 30 April in F1.3 instead.

Week 10

I gave ye a one page summary of further differentiation and an error analysis worked example. We began our study of further integration by looking at integration by parts and integrals involving the inverse trigonometric functions.

Week 11

In Week 11 we will finish our work with the inverse trigonometric functions and begin to look at applications of integration to work.

Week 13

In Week 13 we will go through the Autumn 2012 paper.

Test 2

We will have test 2 on the entirety of the further differentiation material on Wednesday. Please find a sample.

Notes

A relatively recent set of MATH6040 lecture notes. You might find this E-book useful.

Math.Stack Exchange

If you find yourself stuck and for some reason feel unable to ask me the question you could do worse than go to the excellent site math.stackexchange.com. If you are nice and polite, and show due deference to these principles you will find that your questions are answered promptly. For example this question that I addressed but didn’t properly address in class.

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.

Weeks 9

In Week 9 we finished our study of partial differentiation — and looked at its applications to error analysis — and spoke about related rates (which I probably should have done first but anyway!). I have a one page summary of further differentiation and an error analysis worked example which I will give you on Tuesday.

Week 10

In Week 10 we will begin our study of further integration by looking at integration by parts.

Test 2

We will have test 2 on the entirety of the further differentiation material in Week 11. Please find a sample. The test will be held on Wednesday April 23.

Notes

A relatively recent set of lecture notes — including related rates and implicit differentiation…also you might find this E-book useful.

Math.Stack Exchange

If you find yourself stuck and for some reason feel unable to ask me the question you could do worse than go to the excellent site math.stackexchange.com. If you are nice and polite, and show due deference to these principles you will find that your questions are answered promptly. For example this question about related rates.

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.

Weeks 7 & 8

In Weeks 7 & 8 we began our study of some further topics in differentiation: namely parametric differentiation, implicit differentiation and partial differentiation.

Week 9

In Week 9 we must finish our study of partial differentiation — look at its applications to error analysis — and talk about related rates (which I probably should have done first but anyway!)

Test 2

We will have test 2 on the entirety of the further differentiation material in Week 11. Please find a sample. This is a tough test: ye have enough to do questions one to three. By the end of Week 9 — or at worst the start of Week 10 you should be able to do all of the questions. The test will most likely be held on Wednesday April 23.

Notes

A relatively recent set of lecture notes — including partial differentiation. Implicit Differentiation notes and exercises are here also…also you might find this E-book useful.

Math.Stack Exchange

If you find yourself stuck and for some reason feel unable to ask me the question you could do worse than go to the excellent site math.stackexchange.com. If you are nice and polite, and show due deference to these principles you will find that your questions are answered promptly. For example this question about parametric differentiation.

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

You are identified by the last five digits of your student number.

Week 6

In Week 6 we finished off vector algebra. Hopefully you won’t forget this image:

Note that the cross product of two vectors is perpendicular to both of the vectors — the same way the toilet roll holder is perpendicular to both of my arms here… the ‘toilet roll vector’ is in the same direction as in this picture:

Week 7

In Week 7 we will begin our study of some further topics in differentiation: namely related rates, parametric differentiation, implicit differentiation and partial differentiation.

Notes

A relatively recent set of lecture notes, with gaps.

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 1

The test will be held this week Wednesday 6 March). Please find a sample. The sample is to give you an idea of the format and length.

Week 5

In Week 4 we will continued our study of Vector Algebra including the Cross Product. We saw that vector algebra has applications to mechanics such as the fact that work can be written and torque/moment of a force is defined as .

Week 6

In Week 5 we will finish off vector algebra, have our test and start a review of MATH6015 material: differentiation.

Test 2

Ye will get two weeks of notice for test 2 and it will be on differentiation.

Notes

A relatively recent of lecture notes, with gaps.

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 be held in Week 6 (Wednesday 6 March). Please find a sample. I have decided that the test will be on matrices only so everything in Chapter 1 is examinable. The test will be 50 minutes long. The sample is to give you an idea of the format and length.

Week 3

In Week 4 we will begin our study of Vector Algebra.

Week 4

In Week 4 we will continue our work on Vector Algebra including the Cross Product.

Tutorials

I have made a promise that I will make the matrix inverse easier to compute like the examples on p.22 and 23… this will be the case.

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 3

We learned how to use the matrix inverse to solve simultaneous equations. We also introduced Cramer’s Rule which is a method that is useful if you only want to find one of the variables rather than all of them. Cramer’s Rule uses determinants and we showed how to calculate the determinant of and matrices. We also explained that when the determinant of the coefficient matrix is zero, the Gauss-Jordan algorithm cannot work because the matrix is not invertible.

Week 4

In Week 4 we will begin our study of Vector Algebra.

Tutorials

If we can do the question on page 43 of the notes, then you are in a good place for matrix algebra. I have made a promise that I will make the matrix inverse easier to compute like the examples on p.22 and 23.

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.

Tutorials

I am going to take attendance from now on particularly at Friday’s tutorial. If there are more than 15 people at a Friday tutorial then the best-attending surplus will be invited to go to the Tuesday tutorial. There were only 14 at today’s tutorial so the BIS are on their own this Tuesday and all of the Bio are to attend their tutorial on Friday.

Week 1

In week 1 we introduced the idea of a matrix and explored some of the algebra of matrices such as addition, scalar multiplication, transpose and multiplication.

Week 2

In Week 2 we introduced the idea of the inverse of a matrix. If we want to calculate the inverse of a matrix we do the Gauss-Jordan algorithm. Why the Gauss-Jordan algorithm works is answered in the language of elementary matrices and row operations.

Next Week

We see how to use matrix inverses to solve simultaneous equations; e.g.

Notes

Please find attached.