# SECTION 7.3# Example 1 F := s -> b/(s^2+b^2);

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F(s-a);

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# Example 2f := t -> sin(b*t);

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fprime := D(f);

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fprime(t)/b;

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Lfprime := s*F(s)-f(0); #Theorem 4

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Lcosbt := %/b;

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# Example 4F(s); # Laplace transform of sin(b*t)

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-D(F)(s); # Laplace transform of t*sin(b*t), by Theorem 6

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