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Partial Differential Equations

Partial Differential Equations

Suppose that a string of length L is held fixed at one end and is being moved up and down, say with a displacement of f(t), at the other end. Assume that the string is initially at rest and has a zero displacement, and similarly, that the forcing of the string, f(t), also has a zero initial velocity and displacement. a) Write

Partial Differential Equation (PDE) : Heat Conduction

3. Consider the PDE problem: {see attachment} Suppose v(x,y) represents the temperature of some heat-conducting material. What physical scenario could be described by this PDE problem? What does each equation mean physically? Solve for v(x,y). Your final answer should indicate how all constants are obtained from g(x).

Partial length of chord

I have a circle, diameter and radius unknown. It has a chord running through the center (point "O") and the end points are on the circle. Lets call this chord "SR" This chord SR bisects another chord "TU" and TU has midpoint "K". The only other information I have is that arc angle "TR" formed by point "T" from chord TU and point

Impulse Forcing

You have a mass-spring system, a unit impulse is applied to this system (at equilibrium,at rest) and the response is recorded and determined to be (10e^-0.1t)- (10e^-0.2t) In general terms what does the form of the impulse response function tell you about the system?

Differential Equation: Partial Integrals

For this problem state the menthod you used and show the work required to obtain the answer. Find the complete solution to each of the equation problem: 4y^2 - 4y^1 + y = e^(x/2) * square root of (1-x^2)

Proving a partial order and total order.

In each of the following say whether or not R is a partial order on A. If so, is it a total order? a) A= {a,b,c,d}, R= {(a,a),(b,a),(b,b),(b,c),(c,c)} b) A is the set of positive divisors of 24, that is A= {1,2,3,4,6,8,12,24}, and the relation R is dividing. If B is the set of positive divisors of 24 except 1, what is the