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 Equations...
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 [Broken]
Solutions are here.
http://www2.imperial.ac.uk/~bin06/M2...insoln2008.pdf [Broken]
My first question is about 3(ii), the proof of Cauchy's integral formula for the first derivative.
The proof here uses the deformation...
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...
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?
Explain why, in a perfectly competitive labor market, the total net advantages of all occupations would be equalized. (10)
In a perfectly competitive labor market, all workers have the same wage. So if they have the same wage how can net advantages be equalized? Jobs which have bad working...
Is the answer I = \frac{Q}{RC}.
I neglected the negative like they did in the question. Why do they get rid of the negative when we talk about activity? Is it because we need it when using differential equations because it is decaying but we leave it when not using the differential equation...
Homework Statement
The discharge of a capacitor through a resistor is analogous to radioactive decay.
Write down the equation for capacitor discharge which is analogous to A = \lambda N.
Explain the analogy between A and the subject of your equation.
Homework Equations
The...
I'm unsure about the equation Q = It (charge = current * time). Say we have a perfect circuit with minimal resistance. The current will stay constant and never run out. Work doesn't need to be done because no resistance needs to be overcome. But then, as time goes on, the charge increases...
But if we do it with vectors for non-constant angular velocity isn't it kind of the same as the way I did in the first post (take x and y separately and combine them with Pythagorean theorem)?
I haven't learned about complex numbers and polar co-ordinates yet. I find it interesting that complex numbers (which seem abstract and not that relevant in the real world) are good at describing circular motion. I thought they were only used in really advanced level physics.
For uniform...
Is this derivation correct?
I managed to derive v = r \omega and (I think) a = \omega^2 r.
I did a^2 = \ddot{x}^2 + \ddot{y}^2 to get eventually
a^2 = r^2(\dot{\theta}^4 + \ddot{\theta}^2). Then I said that, for uniform circular motion, the angular velocity \dot{\theta} is a constant...
http://www.s-cool.co.uk/alevel/physics/capacitors/time-constant-and-energy-stored-in-capacitors.html [Broken]
Note: the energy used by the cell to charge the capacitor, W = QV, but the energy stored on the capacitor = 1/2 QV. So half the energy is lost in the circuit as heat energy as the...
Why is it E = \frac{1}{2} C V^2? I mean why is it half? It seems to arise from integration but can't we say that Q = CV and then multiply both sides by V to give QV = CV^2? The left hand side is equal to work done because voltage is defined by work done/charge.
Thanks. I managed to do that part. Are the co-ordinates of P
P (1 + \csc \theta + \cot \theta, 0)?
I can't do part (ii). For the explanation I'm unsure. All I know is that angle PRO (in the B area) is \frac{\pi}{2} - \theta.
I got A(\frac{\pi}{4}) = 1 + \sqrt2 -\frac{3\pi}{8}. Is that correct?
http://www.maths.ox.ac.uk/filemanager/active?fid=2929 [Broken]
Question 4 on page 12.
Could someone give me some hints on how to do this? I have no idea how. All I know is that we could draw a line from the center of the circle to Q, which I think would be perpendicular to that tangent. Also...