You are currently browsing the category archive for the ‘MATH6040’ category.
Week 8
We added two techniques to our antidifferentiation skills:
- Integration by Parts (a fourth method)
- Complete the square (a special manipulation)
We had about an hour of tutorial time.
Homework/Study
I would strongly recommend completing the following:
I would invite you to try
- p.123, Q.1-6
- p.130, Q.1-8
Additional exercises p.124, Q.7-8, and harder exercises Q. 9-11
You may have some of these done in class.
Please feel free to ask me questions about the exercises via email. In addition, you can hand up your work in class and I will have it correct for the week after.
Week 9
We will look at some applications of integration:
- work
- centroids of laminas and
- centres of gravity of solids of revolution
We may or may not have additional tutorial time.
Outlook
We will start Chapter 4 in Week 10, and Test 2, on Chapter 3, will be in Week 11. A sample test 2 will appear in Week 9. To make Test 2 easier you will be prompted in what technique (tables, manipulation (inc. complete the square), 
Study
Please feel free to ask me questions about the exercises via email.
Student Resources
Please see Student Resources for information on the Academic Learning Centre, etc.
Week 7
We started with a Chapter 2 Concept MCQ.
We started Chapter 3, on Integration. We worked on material that is technically revision from last semester… but because of the rushed nature of MATH6012 I didn’t expect students to be very competent in the material… but actually it seems ye knew more than I had hoped. It is material that is important for Level 7.
We had 45 minutes of tutorial time.
Homework/Study
I would strongly recommend completing the following:
I would invite you to try
- p.118, Q.1-13
You may have some of these done in class.
Please feel free to ask me questions about the exercises via email. In addition, you can hand up your work in class and I will have it correct for the week after.
Week 8
We will add two techniques to our antidifferentiation skills:
- Integration by Parts (a fourth method)
- Complete the square (a special manipulation)
Outlook
In Week 9 we will look at some applications of integration:
- work
- centroids of laminas and
- centres of gravity of solids of revolution
We will start Chapter 4 in Week 10, and Test 2, on Chapter 3, will be in Week 11. A sample test 2 will appear in Week 9.
Study
Please feel free to ask me questions about the exercises via email.
Student Resources
Please see Student Resources for information on the Academic Learning Centre, etc.
Test 1 Results
Are released on Canvas.
Test 2 will be in Week 11 and will examine Chapter 3 (which will be covered in Weeks 7-9).
Week 6
We finished Chapter 1 by talking about determinants and Cramer’s Rule.
We had about an hour and a half of tutorial time.
Read the rest of this entry »Test 1 Results
Should be released on Canvas at some stage this week. Test 2 will be in Week 11 and will examine Chapter 3 (which will be covered in Weeks 7-9).
Week 5
We had Test 1.
We looked at linear systems. We had about an hour of tutorial time.
Read the rest of this entry »Test 1 Monday 21 February
Please see Canvas —> MATH6040 —> Assignments for more information.
Lectures on Chapter 2 will continue at 20:25.
Week 4
For technical reasons, we were unable to have the Concept MCQ about vectors so we started by looking at Chapter 2: Matrices. We did some examples of matrix arithmetic and looked at Matrix Inverses — “dividing” for Matrices. This allowed us to solve matrix equations.
Some deeper discussion here:
Why do we multiply matrices like we do?
We had no tutorial time (bar Example 4 on p.71).
Read the rest of this entry »In theory (see Learner Workload) you are supposed to spend seven hours per week on MATH6040. I know this might not be possible for everyone, but there is no doubt that spending four hours per week on exercises is going to be best for your learning. Any questions, please email.
Test 1 – Week 5
Please see Canvas —> MATH6040 —> Assignments for more information.
Week 3
Lecture
In Week 3 we finished Chapter 1, and the material for Test 1, by talking at the applications of vectors to work and moments
We had an hour and a half of tutorial time on the p.47 and p.40 Exercises.
Exercises
How much time you put into homework is up to you: of course the more time you put in the better but we all have competing interests. Please feel free to ask me questions about the exercises:
- Sample Test 1, p.56-61 (gives an idea of layout and length only)
- p. 47, Q.1-6
There is an applet to play with:
Additional questions include:
- p. 49, Q.7-14
There are more questions to be found in Weeks 1 and 2.
Additional practise questions (beyond the manual) may be found by looking at past MATH6040 exam papers.
Week 4
We will start at 19:05 with a Vectors Concept MCQ.
We will start looking at Chapter 2: Matrices. We will some examples of matrix arithmetic and look at Matrix Inverses — “dividing” for Matrices. This will allow us to solve matrix equations.
We will likely have no tutorial time.
Study
Please feel free to ask me questions about the exercises via email.
Student Resources
Please see Student Resources for information on the Academic Learning Centre, etc.
In theory (see Learner Workload) you are supposed to spend seven hours per week on MATH6040. I know this might not be possible for everyone, but there is no doubt that spending four hours per week on exercises is going to be best for your learning. Any questions, please email.
Week 2
Lecture
In Week 2 we finished talking about the scalar product before talking about the vector product.
We had about thirty minutes tutorial time on the p. 30 exercises.
Exercises
How much time you put into homework is up to you: of course the more time you put in the better but we all have competing interests. Please feel free to ask me questions about the exercises:
- p.30-32, Q.1-11. The starred Q.12* might be a little harder the way it is set up.
- p.40, Q.1-5
There are applets to play with:
Additional questions include:
- p.32, Q.12* — you may need the formula that the area of a triangle is equal to
.
- p.40, Q.6-11
Week 3
In Week 3 we will look at the applications of vectors to work and moments
We will manage more tutorial time.
Test 1
The test will be in Week 5. More official notice will be given in Week 3. There is a sample test on p.56 of the manual.
Study
Please feel free to ask me questions about the exercises via email.
Student Resources
Please see Student Resources for information on the Academic Learning Centre, etc.
In theory (see Learner Workload) you are supposed to spend seven hours per week on MATH6040. I know this might not be possible for everyone, but there is no doubt that spending four hours per week on exercises is going to be best for your learning… but this week’s exercises could be done by you in a matter of minutes.
Week 1
Lecture
We began our study of Chapter 1, Vector Algebra by studying the difference between a scalar (single number) and a vector (list of numbers). We looked at how to both visualise vectors and describe them algebraically. We learned how to find the magnitude and direction of a vector, add them and scalar multiply them. We spoke about displacement vectors and introduced the vector product known as the dot product.
Exercises
How much time you put into homework is up to you: of course the more time you put in the better but we all have competing interests. Please feel free to ask me questions about the exercises:
- p.30, Q. 1-2
You could also play with this applet. See the top of p.21 of the manual for details.
Week 2
In Week 2 we will finish talking about the dot product and we might start talking about the vector product.
Test 1
If we finish the Vectors chapter in Week 3 the test will be in Week 5 (this is very likely): otherwise we will push this out to Week 6. Official notice will be given in Week 3 (or Week 4 if necessary). There is a sample test on p.56 of the manual.
Study
Please feel free to ask me questions about the exercises via email.
Student Resources
Please see Student Resources for information on the Academic Learning Centre, etc.
Differentiation Test
Test Tuesday 20 April 19:30 to 20:45. Five questions, one for each of the five sections in Chapter 3.
You can find old (e.g. Chapter 3) videos on my YT channel here. (Links to an external site.)
One more video that is actually Chapter 3 material (and the recording was a little messed up so no live writing… a new version will be in the Week 11 lectures.):
Week 10
Lectures
Revision of integration and integration by parts.
- Revision of Integration (Links to an external site.) (44 minutes)
- Integration by Parts (Links to an external site.) (36 minutes)
Here are last year’s lectures of the same material:
- Revision of Antidifferentiation: Direct and Manipulation (Links to an external site.) (27 minutes)
- Revision of Antidifferentiation: Substituion (Links to an external site.) (22 minutes)
- Integration by Parts (Links to an external site.) (30 minutes)
I recorded a lot of this material before in a live lecture: press here to watch live version (Links to an external site.) (84 minutes).
Exercises
How much time you put into homework is up to you: of course the more time you put in the better but we all have competing interests. Please feel free to ask me questions about the exercises.
Try:
- p. 165, Q.1-13
- p. 171, Q.1-5
Additional Exercises: p. 171, Q. 6-9
Submit work for Canvas feedback by Sunday 18 April for video feedback after Monday 19 April.
Outlook
Week 11
Perhaps of the order of 1.5 hours of lectures on completing the square (Links to an external site.), and work (Links to an external site.).
Week 12
Perhaps of the order of 1.5 hours of lectures on centroids (Links to an external site.) of laminas and centres of gravity of solids of revolution (Links to an external site.).
Weeks 13 and 14
I will continue to provide learning support.
Assessment Schedule
Week 11 – 25% Differentiation Test (Zoom Tutorial in Week 10, after Easter)
Week 14 – 25% Integration Test (Zoom Tutorial in Week 13)
Study
Please feel free to ask me questions about the exercises via email. I answer emails every morning seven days a week.
Student Resources
Please see Student Resources (Links to an external site.) for information on the Academic Learning Centre, etc.
Easter might provide extra time to put into Chapter 3.
Matrices Test — Corrections
I have a bit of a backlog of corrections but hopefully I can get these to ye before Easter Sunday.
Week 9
Lectures
Final two sections of Chapter 3:
- Partial Differentiation I (31 minutes)
- Partial Differentiation II (38 minutes)
- Error Analysis using Differentials (30 minutes)
- Error Analysis Example (5 minutes)
Here are last year’s lectures of the same material:
- Functions of Several Variables (12 minutes)
- Partial Differentiation: Theory (25 minutes)
- Partial Differentiation: Examples (11 minutes)
- Higher Order Partial Derivatives (21 minutes)
- Partial Differentiation Tutorial (9 minutes)
- Differentials (10 minutes)
- Propagation of Errors (7 minutes)
- Propagation of Error Examples (25 minutes)
Exercises
How much time you put into homework is up to you: of course the more time you put in the better but we all have competing interests. Please feel free to ask me questions about the exercises.
Try:
- p. 143, Q. 1-5 [Note these exercises are interleaved – there are questions here from earlier sections in Chapter 3]
- p. 150, Q. 1-6 [Note these exercises are interleaved – there are questions here from earlier sections in Chapter 3]
Additional Exercises: p. 143, Q. 6, p. 151, Q.7-8, 9-10
Submit work for Canvas feedback by Sunday 28 March for video feedback after Monday 29 March.
Outlook
I will be providing learning support over Easter.
Looking further ahead, to after Easter, a good revision of integration/antidifferentiation may be found here. Here is some video of revision of antidifferentiation.
Week 10
Perhaps of the order of 1.5 hours of lectures on starting Chapter 4 on (Further) Integration with a revision of antidifferentiation, and a look at Integration by Parts. We will use implicit differentiation to differentiate inverse sine.
Week 11
Perhaps of the order of 1.5 hours of lectures on completing the square, and work.
Week 12
Perhaps of the order of 1.5 hours of lectures on centroids of laminas and centres of gravity of solids of revolution.
Assessment Schedule
Week 11 – 25% Differentiation Test (Zoom Tutorial in Week 10, after Easter)
Week 14 – 25% Integration Test (Zoom Tutorial in Week 13)
Study
Please feel free to ask me questions about the exercises via email. I answer emails every morning seven days a week.
Student Resources
Please see Student Resources for information on the Academic Learning Centre, etc.
J.P. McCarthy: Math Page 
Recent Comments