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

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) d)Why is it not possible to termwise differentiate your series from part (a) to get the Fourier series representation of the function 1? (Make sure you are clear on what the Fourier series for 1 is)