Quaternions and other mathy doohickies

[Guest]

Originally posted by Ramo
A complex function is differentiable if and only if the partial of the real part of the function with respect to real part of the variable is the partial of the imaginary part of the fuction with respct to the imaginary part of the variable and the partial of the imaginary part of the function with respect to the real part of the variable is the negative of the partial of the real part of the function with respect to the imaginary part of the variable.

Words to live by...

Cauchy Riemman Equations
What do you study Ramo?

[Guest]

No Rogan
in a set all elements are non-identical
if a set of 3 elements has 2 that are identical, its cardinality is defined as being less than 2 ....
So suppose we have two sets : A {1,2,3} and B {4,5,6}
there are 6 bijections (one to one functions) beetween them
1 - > 4
2 - > 5
3 - > 6

1 - > 4
2 - > 6
3 - > 5

1 - > 5
2 - > 4
3 - > 6

1 - > 5
2 - > 6
3 - > 4

1 - > 6
2 - > 4
3 - > 5

1 - > 6
2 - > 5
3 - > 4

And they form a group, of order 6, usually known as the Symmetric group of order 6 (the group of permutations of 3 elements) which is isomorphic (the same up to notation) as the group of symmetries of an equilateral triangle.
Suppose we have two equilateral triangles, with the vertices labeled as the sets before
so one trinagle with vertices 1,2,3 and the other 4,5,6
there are 6 ways to send one triangle so its exactly on top of the other which correspond to the 6 ways listed above.
If the triangle is not equilateral there will be less (2 ways actually for an isoceles triangle and one way for a scalen (sp?) )
even though the numbers in the set are all different (they have to be, they are used as labelling)

[Ramo]

LT, I'm an undergrad in physics and math. Primarily physics though (that's what I plan on going to grad school in).

[KrazyHorse]

Originally posted by Ramo
A complex function is differentiable if and only if the partial of the real part of the function with respect to real part of the variable is the partial of the imaginary part of the fuction with respct to the imaginary part of the variable and the partial of the imaginary part of the function with respect to the real part of the variable is the negative of the partial of the real part of the function with respect to the imaginary part of the variable.

Words to live by...

You should only be dealing with harmonic functions anyhow. Simply analytic and differentiable finctions aren't very interesting.

[Ramo]

True. We've just started power series and the like.

[Guest]

Have you done any algebra?
jsut how much algebra is useful in physics anyway?
I think some basic group theory for quantum mech or something ?

[Ramo]

I'm taking an algebra class right now. True, group theory is pretty essential in quantum mechanics, but it's not that useful at the undergrad level. I won't need it for another year.

[Dinner]

This thread reminds me why I hated differential equations. Those bastards at the uni made me take it before they'd give me my science degree.

[KrazyHorse]

As well they should have.

[Dinner]

That doesn't mean I can't loath them for it.

[KrazyHorse]

Admittedly I feel the same way about my PDE course.