Arguably, the three central concepts in the theory of differential calculus are that of a function, that of a tangent and that of a limit. Here we introduce functions and tangents.

Functions

When looking at differential calculus, two good ways to think about functions are via algebraic geometry and interdependent variables. Neither give the proper, abstract, definition of a function, but both give a nice way of thinking about them.

Algebraic Geometry Approach

Let us set up the plane, \Pi. We choose a distinguished point called the origin and a distinguished direction which we call ‘positive x‘. Draw a line through the origin in the direction of positive x. This is the x-axis. Choose a unit distance for the x-direction.

Now, perpendicular to the x-axis, draw a line through the origin. This is the y-axis. By convention positive y is anti-clockwise of positive x. Choose a unit distance for the y-direction.

This is the plane, Pi:

axes.jpg

Now points on the plane can be associated with a pair of numbers (a,b). For example, the point a distance one along the positive x and five along the negative y can be denoted by the coordinates (1,-5):

point.jpg

Similarly, I can take a pair of numbers, say (-1,3), and this corresponds to a point on the plane.

This gives a duality:

points on the plane $lates \Leftrightarrow$ pairs of numbers

Now consider the completely algebraic objects

x=3\,,\,\,y=2\,,\,\,y=x\,,\,\,y=x^2\,,\,\,y=x+2\,,\,\,x^2+y^2=1.

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Assessment 5

Assessment 5 will be on Tuesday, 6 December 2016.

The following  group will sit the assessment at 17:15 (arrive around 17:05):

  • COMP1B-X

The following group will sit the assessment at 18:15 (arrive around 18:05)

  • COMP1B-Y

Keep an eye on your CIT Blackboard and email for the latest and definitive assessment information.

Week 12

We looked at graphing and mathematical modelling.

Week 13

Two tutorials:

  • COMP1B-Y: Monday 10:00 in F1.3
  • COMP1B-X: Monday 15:00 in B251
  • COMP1B-X and 1B-Y: Tuesday 14:00 in B225

Study

Please feel free to ask me questions about the exercises via email or even better on this webpage.

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc.

Continuous Assessment Marks

I will send you an email either today or Monday regarding your continuous assessment marks.

Week 12

We finished the quick section on mean and root-mean-square values and then we spoke about differential equations.

Week 13 – Revision

  • Tuesday 09:00 in B149
  • Thursday 09:00 in B180
  • Thursday 11:00 in B188

Sadly you have lost out on a tutorial and an extra revision class due to the test you have on Week 13.

The review will be given over to going over last year’s paper (at the back of your notes). If the paper is completed I will take questions from the class. If there are no questions I will help one-to-one.

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Week 12

We looked at sampling and hypothesis testing.

I sent you a very important email about your continuous assessment marks. Please read it.

Week 13

We will go through last year’s exam on the board and then I will answer your questions if there are any. If there are none I will help one-to-one. Usual class times and locations.

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You will need graph paper for the remaining MATH6000 classes. I advise that you gang up and buy graph paper together in the shop downstairs.

Assessment 4 Results

If you require a result of 40% or more on Assessment 5, you will receive an email regarding your results on or before Wednesday. Otherwise you must wait until your results are released, in January.

Assessment 5

Assessment 5 will be on Tuesday, 6 December 2016.

The following  group will sit the assessment at 17:15 (arrive around 17:05):

  • COMP1B-X

The following group will sit the assessment at 18:15 (arrive around 18:05)

  • COMP1B-Y

Keep an eye on your CIT Blackboard and email for the latest and definitive assessment information.

Week 11

We began our study of coordinate geometry.

Week 12

We will look at graphing and mathematical modelling.

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Assessment 2 Results

Have been sent to you. Some comments here

Week 11

We looked at the BinomialPoisson and Normal Distributions.

Week 12

We will look at sampling and hypothesis testing.

Week 13

We will go through last year’s exam on the board and then I will answer your questions if there are any. If there are none I will help one-to-one. Read the rest of this entry »

Test 2 Results.

Probably on Monday

Week 11

We had a quick section on volume and then we spoke about applications to work. We started looking at the mean value of a function.

Week 12

We will finish the quick section on mean and root-mean-square values and then we will talk about differential equations.

Week 13 – Revision

Tutorial times and venues as normal.

The lecture times will be given over to going over last year’s paper (at the back of your notes). When the paper is completed I will take questions from the class. If there are no questions I will help one-to-one.

Read the rest of this entry »

Assessment 4

Assessment 4 will be on this Wednesday, 23 November 2016.

The following  group will sit the assessment at 17:15 (arrive around 17:05):

  • COMP1B-X

The following group will sit the assessment at 18:15 (arrive around 18:05)

  • COMP1B-Y

Keep an eye on your CIT Blackboard and email for the latest and definitive assessment information.

Week 10

We looked at scientific notation, unit conversion and logarithms.

Week 11

We will finish our study of logarithms and begin our study of coordinate geometry.

Study

Please feel free to ask me questions about the exercises via email or even better on this webpage.

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc.

Assessment 2

Assignment 2 submissions to be left on my desk in A283 by 18:00 on Monday. I should be in the room 09:00-10:00, 11:00-13:00 and 14:00-15:00.
There are four other lecturers in this office so hopefully somebody will be there if you come outside this time. There is a class at 13:00 on Monday in A213B into which you can also drop your submission.
 
I do want a print out of the Excel work and please email the Excel work to me also.

Work submitted to A283 after 18:00 on Monday 21 November will be assigned a mark of zero. Hand up whatever you have on time.

Catch-Up Class

At the moment we are down 2.5 hours due to a number of missed classes. We will make one hour up on Tuesday 22 November at 16:00 in B180.

Week 10

We applied what we learnt to error analysis.

Week 11

We will start the last chapter on probability and statistics. We will look at the BinomialPoisson and Normal Distributions.

Study

Please feel free to ask me questions about the exercises via email or even better on this webpage.

Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc.

 

 

 

Test 2

The second 15% test will take place at 9 am Tuesday 22 November in B149 (Week 11). A slight change in format to last year: this year the format will be as per this sample (although there will be space to write your answers into).

You will be given from 09.05 — 10.00. You will be given a copy of these tables.

Week 10

We finished substitution and started partial fractions.

Week 11

We will have a quick section on volume and then we will talk about applications to work.

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J.P. McCarthy Maths

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