In: Advanced Math
My instructor doesn't have the most intelligible answer keys. Could you explain how to solve this?
Math 266, Quiz 15: Answers due today, April 22, by 1:00 PM via email.
1. Let g(t) be given by
?(?) = {
0, 0 < ? < 1
? − 1, 1 < ? < 2
3 − ?, 2 < ? < 3
1, ? > 3
Rewriting ?(?) using the unit step function gives:
a) ?(?) = (? − 1)?(? − 1) + (4 − 2?)?(? − 2) + (? − 2)?(? − 3)
b) ?(?) = (? − 1)?(? − 1) − (? − 1)?(? − 2) + (? − 3)?(? − 2) − (? − 3)?(? − 3) + ?(? − 3)
c) ?(?) = (? − 1) − (? − 1)?(? − 2) + (3 − ?)?(? − 2) − (3 − ?)?(? − 3) + ?(? − 3)
d) ?(?) = (? − 1)?(? − 1) + (1 − ?)?(? − 2) − (? − 3)?(? − 2) + (? − 3)?(? − 3)
e) None of the above.
2. Use Laplace transforms to solve ?′′ + ? = ?(? − 1) − ?(? − 2) with ?(0) = 0, ? ′ (0) = 1