LAPLACE TRANSFORM Problem 1. Compute the Laplace Transform of fir) = (2-4). 2. Compute the Laplace...

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LAPLACE TRANSFORM Problem 1. Compute the Laplace Transform of fir) = (2-4). 2. Compute the Laplace Transform of f(1) = sin(ex+0). 3. Compute the Laplace Transform of f(t)=rsinh(4/). Hint: Use c{r}-(-1){FG)} where F(s) = C{RO}. 4. Compute the Laplace Transform of f(t)= te cos(21). 5. Compute the Laplace Transform of f()-sin(3) 6. Compute the Laplace Transform of (0)-e" sin(3). 7. Compute the Laplace Transform of 20(1-4). where U is the unit step function. Hint: Use c{80-a)}-e "C{1+a)} 8. Compute the Laplace Transform of (-r+2)U(-1). where U is the unit step function. 9. Compute the Laplace Transform of (3)U(1-2). where U is the unit step function. 10. Compute the Laplace Transform of 2 if0st <1 - iflsi Let y(t) be the solution of the initial-value problem y'=f(t,y), y (to)=yo. Euler's method for finding approximate values of y(t) is Yk+1=Yk+hf (tkryk). However, the quantity yk+hf (tkyk) is never computed exactly: we always in- troduce an error &k with |k| LAPLACE TRANSFORM Problem 1. Compute the Laplace Transform of fir) = (2-4). 2. Compute the Laplace Transform of f(1) = sin(ex+0). 3. Compute the Laplace Transform of f(t)=rsinh(4/). Hint: Use c{r}-(-1){FG)} where F(s) = C{RO}. 4. Compute the Laplace Transform of f(t)= te cos(21). 5. Compute the Laplace Transform of f()-sin(3) 6. Compute the Laplace Transform of (0)-e" sin(3). 7. Compute the Laplace Transform of 20(1-4). where U is the unit step function. Hint: Use c{80-a)}-e "C{1+a)} 8. Compute the Laplace Transform of (-r+2)U(-1). where U is the unit step function. 9. Compute the Laplace Transform of (3)U(1-2). where U is the unit step function. 10. Compute the Laplace Transform of 2 if0st <1 - iflsi LAPLACE TRANSFORM Problem 1. Compute the Laplace Transform of fir) = (2-4). 2. Compute the Laplace Transform of f(1) = sin(ex+0). 3. Compute the Laplace Transform of f(t)=rsinh(4/). Hint: Use c{r}-(-1){FG)} where F(s) = C{RO}. 4. Compute the Laplace Transform of f(t)= te cos(21). 5. Compute the Laplace Transform of f()-sin(3) 6. Compute the Laplace Transform of (0)-e" sin(3). 7. Compute the Laplace Transform of 20(1-4). where U is the unit step function. Hint: Use c{80-a)}-e "C{1+a)} 8. Compute the Laplace Transform of (-r+2)U(-1). where U is the unit step function. 9. Compute the Laplace Transform of (3)U(1-2). where U is the unit step function. 10. Compute the Laplace Transform of 2 if0st <1 - iflsi Let y(t) be the solution of the initial-value problem y'=f(t,y), y (to)=yo. Euler's method for finding approximate values of y(t) is Yk+1=Yk+hf (tkryk). However, the quantity yk+hf (tkyk) is never computed exactly: we always in- troduce an error &k with |k| Let y(t) be the solution of the initial-value problem y'=f(t,y), y (to)=yo. Euler's method for finding approximate values of y(t) is Yk+1=Yk+hf (tkryk). However, the quantity yk+hf (tkyk) is never computed exactly: we always in- troduce an error &k with |k|