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Consider how you determined how many lobsters can fit along the length of the crate. How many lobsters can be packed in one crate the same way as in the diagram
Determine reflexive, symmetric, antisymmetric, transitive, partial order and equivalence. Let R = {(1,1)(3,1)(2,2)(1,2)(3,3)(3,2)} on Z = {1,2,3}
Find the solutions of the differential equations :- (a) x + x = H ( t - 1 ) x (0) = 0
Find the solution of the equation (D2 - D'2 + D - D')z = e^(2x + 2y).
In general terms what does the form of the impulse response function tell you about the system?
At any given time, which part of the rod will be the warmest? Estimate when the maximum temperature of the rod will be less than 1% of T.
Describe what happens when f(t)= 1- cos(cpt/L).
Verify that the Cauchy-Riemann equations ux = vy and uy = -vx are satisfied at the origin z = (0, 0).
Classify and find general expressions for the characteristic coordinates for the equation uxt+tutt+sin(x+1)=0
The PDE is: (1+q^2)u-xp=0. I need to find the solution which passes contains the curve x^2=2u and y=0.
The Cauchy-Riemann equation is the name given to the following pair of equations, ?u/?x=?v/?y and ?u/?y= -?v/?x which connects the partial derivatives.
Check your answer by plugging it back into the equation. x (?u/?x) + y (?u/?y) = 0
What would the solution of the following problem look like for various values of time?PDE utt=uxx 0
List the ordered pairs that belong to the relation.
Partial differential equation PDE Utt = Uxx+sin(3px) 0
Separation of Variables. By using u(x, t) = X(x)T(t) or u(x,y, t) = X(x)Y(y)T(t), separate the following PDEs into two or three ODEs for X and T or X, Y, and T.
Show that the drag force is zero for a uniform flow past a cylinder with circulation.
Suppose: dS = a(S,t)dt + b(S,t)dX, where dX is a Wiener process. Let f be a function of S and t. Show that: df = [(?f/?S)dS + ( ?f/?t+(1/2) +b2(?2f/?S2)] dt
The random component in this random walk can be eliminated by choosing: ?=?V/?S
In solving this problem, derive the general solution of the given equation by using an appropriate change of variables-?u/?t - 2 ?u/?x = 2
Consider the solution of the heat equation for the temperature in a rod given by f(x, t) but with a variable diffusivity.
df/dt+ df/d? +df/de+1=0 Boundary conditions: f as a f(?,e,0)=0
Find the general solution of the wave equation U(tt) = U(xx) subject to the boundary conditions u(0,t) = u(1,t) = 0.
If f(x) = x, 0 < x < ½; and f(x) = ½, ½ < x <1; then what does u(x,y) from problem (1) look like?
Determine the times when the weight will pass through equilibrium.