Question

Problem 1. Find the Laplace Transform of the given function. f(t) = { t, 0 <= t < 1 1, 1 <= t < infinity } Problem 2. Find the inverse Laplace Transform of the given function. F(s) = 2 / (s^2 + 3s - 4) Problem 3. Use the Laplace Transform to solve the given initial value problem. y'' - 2y' + 2y = 0, y(0) = 0, y'(0) = 1. Problem 4. Consider the following function f(t) = -2u3(t) + 4u5(t) - u7(t). a) Write f(t) as a piece-wise defined function. b) Sketch the graph of f(t). c) Find the Laplace Transform of f(t). Problem 5. Solve the following initial value problem. x' = [ -2 1 ; -5 4 ]x, x(0) = [ 1 ; 3 ]

          Problem 1. Find the Laplace Transform of the given function.
f(t) = {
  t, 0 <= t < 1
  1, 1 <= t < infinity
}
Problem 2. Find the inverse Laplace Transform of the given function.
F(s) = 2 / (s^2 + 3s - 4)
Problem 3. Use the Laplace Transform to solve the given initial value problem.
y'' - 2y' + 2y = 0, y(0) = 0, y'(0) = 1.
Problem 4. Consider the following function
f(t) = -2u3(t) + 4u5(t) - u7(t).
a) Write f(t) as a piece-wise defined function.
b) Sketch the graph of f(t).
c) Find the Laplace Transform of f(t).
Problem 5. Solve the following initial value problem.
x' = [ -2 1 ; -5 4 ]x, x(0) = [ 1 ; 3 ]

Problem 1. Find the Laplace Transform of the given function.
f(t) =
t, 0 <= t < 1
1, 1 <= t < infinity

Problem 2. Find the inverse Laplace Transform of the given function.
F(s) = 2 / (s^2 + 3s - 4)
Problem 3. Use the Laplace Transform to solve the given initial value problem.
y” - 2y' + 2y = 0, y(0) = 0, y'(0) = 1.
Problem 4. Consider the following function
f(t) = -2u3(t) + 4u5(t) - u7(t).
a) Write f(t) as a piece-wise defined function.
b) Sketch the graph of f(t).
c) Find the Laplace Transform of f(t).
Problem 5. Solve the following initial value problem.
x' = [ -2 1 ; -5 4 ]x, x(0) = [ 1 ; 3 ]

Added by Diane A.

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