Homework Statement
I am trying to solve this
\begin{align}
d X_t = - b^2 X_t (1 - X_t)^2 dt + b \sqrt{1 - X_t^2} dW_t
\end{align}
where $b$ is a constant.
Note that I have the answer here and can provide it if necessary. But I want to know how one would come up with it.
Homework EquationsThe...
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...
Homework Statement
http://workspace.imperial.ac.uk/mathematics/public/students/ug/exampapers/2010/M2AA2-2010.PDF
Questions 3(iii) and 3(iv)
Homework Equations
The Attempt at a Solution
3(iii)
So here we "guess" that the solution is f = f(r) (f for phi). Then we just have...
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...
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...
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...