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I am a freshman in college and I am in multivariable calculus, I took the first AP calc in highschool. I am deciding to walk in on an Ordinary Differential Equations class. It is apparantly graduate and I didn't understand a single thing in there. I didn't understand anything mainly because I do not know what the symbols represent, and the professor was impossible to understand, (old guy.) Anyways, I took the notes down verbatim and I was wondering if some of you could explain to me what the different sybmols meant...

I understand it is a huge jump from multivariable calculus to ODE, so please no negative comments.

One of the rather longer equations. I believe it was part of a theorem.

[PLAIN]http://mynqa.com/Cargo/eqn.jpg [Broken]

(sorry if it is hard to read, I could not manage the latex form, I will have to learn how to use that sometime)

what is the function [tex]\varphi[/tex](t,[tex]T[/tex],[tex]\varsigma[/tex]) for example?

I also do not understand the inputs to f, what does this equation mean in general?

If it is too difficult to explain in one response, I am also fine with links to websites that could explain, or even reference a book.

I understand it is a huge jump from multivariable calculus to ODE, so please no negative comments.

One of the rather longer equations. I believe it was part of a theorem.

[PLAIN]http://mynqa.com/Cargo/eqn.jpg [Broken]

(sorry if it is hard to read, I could not manage the latex form, I will have to learn how to use that sometime)

what is the function [tex]\varphi[/tex](t,[tex]T[/tex],[tex]\varsigma[/tex]) for example?

I also do not understand the inputs to f, what does this equation mean in general?

If it is too difficult to explain in one response, I am also fine with links to websites that could explain, or even reference a book.

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