Convert the Black-Scholes Equation to the Heat equation ** you MUST use the change of variables specified in the problem!!!

See pdf file for details.

After solving a PDE for the heat equation + a constant - Does the solution to the PDE sugest a simplifying transformation.

See attached PDF file. - This should not take much time at all, I'm betting it's a really simple transformation that won't take two lines to figure out, but PLEASE provide specifics about whatever you do so I can follow the awnser!!! *** TWO PAGES, QUESTION IS ON SECOND PAGE!!!! ****

Show that the form of the Black-Scholes eq. given can be converted into Ut=((sigma^2)/2)*Uxx

Please see attached PDF file. Also ***PLEASE*** DON'T respond with handwritten work, **ONLY*** pdf / word format - mathcad is fine too.

Wave equation

Wave equation problem - show that the wave eq. u(x,t) can be expressed as 1/2((fodd(x+ct)+fodd(x-ct)) - fodd being the odd periodic extension of f(x) See attachment

Differential Equations

Please see attachment

Linear Partial Differential Equation & Linear Homogeneous Partial Differential Equation

Find the General Solution of the equations. (a) r = a2t (b) r – 3as + 2a2t = 0 where r = ∂2z/∂x2 , s = ∂2z/∂x∂y, t = ∂2z/∂y2 (c) (2D2 + 5DD′ + 2D′2)z = 0 (d) ∂3z/∂x3 - 3∂3z/∂x2∂y + 2∂3z/∂x∂y2 = 0 ...continues

Non-linear Partial Differential Equations of order one General method of solution (Charpit’s method )

Solve the differential equation by Charpit’s method : z = px + qy + pq -----------------------------------(1) where p = ∂z/∂x , q = ∂z/∂y

SEND ANSWER AS ATTACHMENT. PDE's.

PDE- SEND ANSWER AS ATTACHMENT What happens on the boundary of the region? Suppose we consider a constant multiple of Z(x, y). Is it still a solution of the PDE? See attachment for question and details

Minimal Surface Equation

attachment works! Send answer as attachment Minimal Surface Equation, please see attachment for equations and questions.

Fourier Series Representation; Termwise Differentiate

(a) Compute the 2[pi]-periodic Fourier series representation for the function x over the interval [-Pi,Pi] (b) Compute (directly) the 2[pi]-periodic Fourier series representation for the function x^2 over the same interval (c) Show how the series in part (a) is related to the termwise-differentiated series from part (b) ...continues