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In general terms what does the form of the impulse response function tell you about the system?
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.
Classify and find general expressions for the characteristic coordinates for the equation.
If f is a real valued function of two variables, the set of points (x, y) for which f(x, y)=c, for some value of the constant c.
What would the solution of the following problem look like for various values of time?
Separation of Variables. By usingu(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.
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?
For k^2 =2(pi)^2, obtain the general form of the solution u(x,y) of the partial differential equation compatible with the boundary conditions.
Verify that each of the given functions is a solution of the given differential equation, and then use the Wronskian to determine linear dependence.
In each direction field above sketch integral curves for which y(o) = -1, y(0) = 1, y(2)=1
Verify that there exists a global solution by invoking the global existence and uniqueness Theorem.
A steel ball weighing 128 pounds (mass= 4 slugs) is suspended from a spring. This stretches the spring 128/485 feet.
Use Laplace Transforms to solve Differential Equation y'' - 8y' + 20 y = t (e^t) , given that y(0) = 0 , y'(0) = 0
Two tanks A and B, each of volume V, are filled with water at time t=0. For t > 0, volume v of solution containing mass m of solute flows into tank A per second
Find two solutions to the initial value problem y, = |y|^(1/2) , y(0) = 0. What hypothesis of the Picard-Lindelöf Theorem is violated?
If air resistance is proportional to the square of the instantaneous velocity, then the velocity v of a mass m dropped from a given height.
Draw a simple NOT, AND, OR circuit in sum of products (SOP) form that represents the equation above.
The production manager has the responsibility of specifying production levels for each product for the coming month.
Formulate a linear programming model that can be used to develop a daily production schedule for the Buffalo and Dayton plants.
Graph the constraints for this problem. Indicate on your graph all feasible mixed-integer solutions.
Draw the Hasse diagram for the partial ordering "x divides y" on the set {3, 6, 9, 18, 54, 72, 108, 162}. Name any least elements, minimal elements.
Discuss several disadvantages of linear programming; clearly explain the reasons for your choices.
Solve the linear programming model by using the computer and determine the sensitivity ranges.
A solution that satisfies all the constraints of a linear programming problem except the nonnegativity constraints is called: