Crash course in LaTeX - this should give you 90% of what you need.
1. On this forum, enclose LaTeX code with math delimiters. The easiest way to do this is to click the Go Advanced button in the lower right. Then you get the TeX button, which will enclose your selection with math delimiters, or you can just click the button and start typing, and the code will be in math delimiters.
Fractions you type this way: \frac{num}{denom}. Exponents you type this way: e^{x}. You can just do e^x, but then if you want you have to type e^{ix}. Subscripts you type this way: x_{n}. To get the fancy L for Laplace Transform, you can do \mathcal{L}. Greek letters are like this: \alpha, \beta, etc. Capital Greek letters are \Alpha, \Beta, etc. Integrals are \int. Line integrals are \oint. Double integrals are \iint. Partial derivative symbols are \partial. If you want nice-looking fractions and integrals, begin the math code with the command \displaystyle. If you want parentheses and braces of any sort to automatically change size to match what's between them, do \left( and \right). Click the Preview Post button while entering math code to see how something looks before you post it.
Finally, on this forum, you can double-click any part of a post that's written in LaTeX in order to see how someone typed it up. For example, here's the first expression from your file (which I did look at), as best as I can make it out:
Make sense?
There's loads more here.