Recent content by gangsta316

Can anybody provide some resources (books, websites etc. - preferably websites or course notes) for a (somewhat rigorous) introduction to Mathematical Finance? Basically, I want to have the background to understand stuff like this http://www3.stat.sinica.edu.tw/library/c_tec_rep/c-2002-10.pdf...

Here are the links: http://www2.imperial.ac.uk/~bin06/M2PM3-Complex-Analysis/m2pm3examination2008.pdf http://www2.imperial.ac.uk/~bin06/M2PM3-Complex-Analysis/m2pm3examinsoln2008.pdf http://www2.imperial.ac.uk/~bin06/M2PM3-Complex-Analysis/m2pm3l18(11).pdf I've been thinking about...

http://www2.imperial.ac.uk/~bin06/M2...nation2008.pdf Solutions are here. http://www2.imperial.ac.uk/~bin06/M2...insoln2008.pdf My first question is about 3(ii), the proof of Cauchy's integral formula for the first derivative. The proof here uses the deformation lemma (from second...

What's the best book for multivariable calculus? I'm a second year undergraduate student in Mathematics. Here is the content: Functions from Rn to Rm: differentiation, contractions, Newton’s method, inverse function theorem, implicit function theorem, higher derivatives...

Thank you. For 3, how about degenerate conics? How can I find the focii and directrices from the standard equation?

Given the equation of a conic section, how can I: 1) find its focii 2) find the equations of its directrices 3) find out what type of conic it is, without using either the arduous matrix method or the equally arduous rotation method To be honest, I don't really like conic sections...

Thank you. I will try those things. Drawing a triangle for the last one seems like a good idea. I thought of that but are we allowed to use H(-x)? The question says that it should be in terms of a(x), b(x) and H(x). Doing that, won't you get tan t = x/2 hence t = arctan (x/2)? I managed to...

Homework Statement http://tinyurl.com/ylor68h I'm having trouble with questions 3, 4, 8, 9 & 10. Homework Equations The Attempt at a Solution For 3 I got (b-dx)/(cx-a) as the inverse and \frac{(x(bc-ad))}{(acx + bc + cdx + d^2)} as the composed function. The bc -...

Why is there an iron core in a transformer? Is it necessary? In a transformer, how does the changing magnetic field on the primary induce a current on the secondary? Can we think of the changing magnetic field causing a changing force on the secondary and causing it to move back and forth...

Thank you. So what does "constant phase difference" mean?

I don't get it. Don't the waves need a constant phase relationship for a stationary wave to be formed? So they are in phase and this is the constant relationship, so why will they ever be out of phase? Aren't all the points in phase? Although I guess it makes sense because they are both...

I think I know what Fleming's left hand rule but how does Fleming's right hand rule come about and why is it opposite for generators? Is Fleming's right hand rule just the left hand rule for electron flow (instead of current) or would it be more proper to use the left hand rule in that case but...

Also, theoretically, do the two waves have to be exactly in phase to produce a stationary wave? And are anti-nodes in phase and nodes out of phase or are they both in-phase (otherwise we wouldn't get a stationary wave) Finally, why is the distance between two adjacent nodes or anti-nodes...

So a stationary wave is produced when both waves are in phase right? Anti-nodes are where both waves are at the peak and nodes are where both waves have 0 amplitude. Is that correct?

I have a question about stationary waves. Anti-nodes are where waves are in phase and nodes are where the waves are out of phase, right? But don't the waves have to be in phase for a stationary wave to be produced (so there wouldn't be any nodes)? Or do they only have to be coherent?