Math and Physics

With all of this free stuff, there had to be a catch somewhere and here it is.

If you're looking at this page then you need help from a professional tutor (like me) unless you want to cover the whole damn lot and work out later what you really need.

If you can barely remember that sine is opposite over hippo.. something or other and you're about to undertake drawing a nurbs polySphere using spherical polar corrdinates, or learning about those things that Mr Hamilton scratched about on the (non-existent) bridge over the Liffy, then you're not as alone as you think. It took me 20 years to realize the biggest problem I had with students, even A-level was ........ they didn't know their tables!

One of my biggest thrills - mathematically speaking - was modelling a piece of hair as a lots of springs and masses in a line. All that stuff about Hooke's law and Newton's second law really works! This thing waved about like a piece of hair. Confirmation to me at last of a lifetime study.

Back into my philanthropic mode, let me try to be a bit more objective.

Math

Start with +ve and -ve numbers: -7 + 5 = -2. -3 x -2 = +6. (Is this guy kidding!)
You'd be surprised. I was going to suggest to make sure you know your tables first, but backed off throught fear of a lambasting.

Think of going above the water as +ve and below as -ve.
So - 3 - 2 = -5 means going under 3 (I don't believe this!) and then under another 2 so you're under the water 5.
Well one of you baying infidels might just answer this :
Just WHY IS -1 x -1 = +1 ?

If you're not too embarrassed to be following on from above, your next step is algebra: -3x - 2x = -5x etc.

Expansion of brackets: 3(x - 2) = 3x - 6.

(x - 1)(x - 2) = x^2 - 3x + 2 etc.

Factorization.Solution of linear & quadratics equations and .... Trigonometry. Lots of it. 3-D trig. Cosine & Sine Rules( for triangles which don't have a right angle) etc. Matrices etc etc.
One day, I'll get some time to complete this list and even put up some notes. How about some quarternions. I'll also put up a good web reference for quarternions some day as well.

Physics

This is easy, since there are only 6 laws in Physics (before Einstein made things complicated) and 4 of them are about electomagnetism which won't bother you in the slightest.

So it comes down to Isaac Newton! His Law of Gravitation and his Three Laws.

His First Law is just a special case of his Second and as far as calculations is concerned, his Third law you just "know" so that leaves only two in the whole of physics and here they are.

1. Every mass attracts every other mass with a force that is directly proptional to the product of the masses .......etc.

2. F = m a

(Force = mass x acceleration.)

Since you won't be doing any calculations with 1. , that just leaves one thing that you have use so I'll shout it louder:

F = M A !!

Just digress a moment to talk about 1. - The Universal Law of Gravitation.
When students don't believe me when I tell them that the coin on the desk is being attracted to the pencil, I tell them I 'm going to show the coin actually MOVE towards another mass - being PULLED - before their very eyes - to another mass!
When they raise their heads of their arms to take a look- yes you probably guessed it - I push the coin over the edge of the table.

But take a look at F = m a.

How do we measure acceleration? With a ruler and a stop-watch.

How do we measure force? mmm... bit tricky. How about a spring for the moment. Stretch it twice as much and the force is twice as much.
(I can hear you saying : hang on, I've heard of Hookes Law - thought you said that there is only one law worth worrying about.
Well I could try to save face and tell you that Hooke's Law is just a result of molecules obeying F= ma (with apologies to Albert), but rather than confuse you, will concede. Learn Hooke's Law as well!
Especially handy when you're trying to model a stand of hair on whats-her-name's head in Tomb Raider or whatever (ah yes Laura Croft's) head.).

Back to F = m a. Isn't it beautiful. Connecting a push and pull (the force) with distance and time! Not only that, if you double one you EXACTLY double the other. (Well it was true until Einstein got pinickity). This is basic nature. The rate at which the speed changes doubles if the push or pull doubles! Why?? !!!

(Please no purist emails about the binomial approximation of Einstein's relativistic mass equation - just imagine that we are still in the time of that super-brained human being pretending to be a tax-collector in the squalid London ale houses.)

That's why we, (make that "I" ) say there are only two laws in Physics - they are the only laws for which we don't know WHY. We can't prove them. We can show that they work, but that's another matter.

Just for the record, here they are again.

1. F = G M m/ r ^2

2. F= m a

Don't I have to know density is mass/volume? Yes you do, but like the rest of physics besides the two laws above, its all man-made. So in order to communicate with each other, I guess you's better read a basic physics book and persevere with all these mutually agreed formulas and defintions if your going to write some code to make a wheel rotate properly as it moves across your screen instead of setting keyframes.

Which topics? Kinematics (very important), Dynamics (our old friend Isaac again) etc etc.
One day I might also put up some tutorials for these, but basically you need to have a basic GCSE knowledge along with some selected A-level topics along with some more interesting stuff like Fresnel Coefficients -which will be of more than passing interest when you are about to write your sub-surface shader. (Which apparently makes a hand look real - I never realized till now that light can bounce around inside a hand!).

This goes for math as well. Best you get a GCSE text book if you need it, for starters.
The BBC BiteSize GCSE site is also very helpful if you can't be bothered ordering from Amazon.