Let L[•] denotes the Laplace transform.
The Laplace transform is a linear operation.
If L[f(t)] = F(s) , then L[f(t −1)] = F(s −1) .
L[(t −2)] = e−s /s .
None of the above statements is FALSE.
x(t)=constant.
x(t)=−ct3 .
x(t)=ct−3 + t .
x(t) = −ce3t + 4t .
Let L[•] denotes the Laplace transform.
All of the above statements are TRUE.
Consider the del operator defined in (6)
All of the above statements are TRUE.
This is a linear ODE.
This is a time-varying ODE.
This ODE has three equilibria.
The equilibria of this ODE are ±1 and ±2 .
Consider the heat equation
Without considering the boundary condition (9.3), a general solution to the
Suppose f(x) = 7sin(3πx) . Then u(x,t)= 7sin(3πx)e−4n2π2t .
Both of the above statements are TRUE.
None of the above statement is TRUE.
Consider the wave equation
Without considering the boundary condition (10.3), a general solution to the
Suppose f(x) = 17sin(9πx) . Then w(x,t) = 17sin(9πx)(sin(27πt)+1) .
Both of the above statements are TRUE.
None of the above statement is TRUE.
(with positive orientation ) will have the largest positive value. (Hint: Use Green’s
Theorem)
(2) Compute this largest positive value.
Compute the least upper bound of the integral
where z is a complex variable, is its complex conjugate, and C denotes the
boundary of a triangle with vertices at the points i3, − 4 and 0, oriented in
counterclockwise direction.
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