ZinZam

Why Maths C is still important

August 27, 2005

Maths is about solving equations, and that is especially true for Queensland Math C.

Surds

Surds are important, they can be used for moving complex numbers and squateroots from the denominator to the numerator. The reason we want to do this is to rationalise the denominator, remember a squareroot squared is a rational number.

Example complex surd:


Example real surd:

Cis notation

Partial fractions

Partial fractions can be used to make complex expressions easier to evaluate

Integration by parts

Cramers Rule

Ironically my ELEC2004 lecturer got annoyed that they skipped over this rule in University Mathematics, but here it is, right from my Math C notebook.

Cramers rule is one of many ways we were taught to solve a system of equations. In the example I have an imaginary set of two simultaneous equations with variables x1 and x2 with answer vector (s1, s2)

Expansion using pascals triangle

I should have never forgotton this, it would've been so useful had I remembered it




This is only a taste of what math C offers. It really is useful stuff for engineering. Other stuff studied includes first order differential equations, more integration, more matrix theory, probability theory etc... It is all stuff used in engineering and computer science.

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Limits

August 17, 2005

Let us for a second cover some theory on limits. Sometimes in mathematics for an infinite sum we can work out a limit and find a real answer that we can express as a known quantity.

For example, the sequence (you need a MathML enabled browser/plugin to view this page)



We can take the limit of:



This gives us the constant


The same can be applied to other systems. Now I pose the following question:

We can construct a snowflake by taking the following steps:

1. Draw a triangle


2. Divide it's side length into three


3. Draw a triangle of 1/3rd length in the middle third of the side



4. Repeat forever




So now heres the questions:

Q. I want to measure the preimeter of the snowflake, what is the answer?

Q. If the side of the original triangle is 1m and I am traveling at 1m/s, how many seconds does it take to have travelled distance but have zero displacement.

Q. If the snowflake's unit length was now 1mm and the atomic radius of a water molecule was close enough to that of a water molecue (0.65Ã…), and the snowflake was densly packed, how long would it now take travelling at 0.001m/s.

Yes these questions have answers, but I won't reveal them until someone has a go at answering them ;)

MathML in Mozilla/Firefox. (There are other plugins for Internet Explorer users on the internet.)

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Back to uni

August 07, 2005

Not much time to come here lately, I really shouldn't be here as much as I am but hum ho,

Testing to make sure I haven't broken this thats all.

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