Rules Summary and Preview.
Laplace Transform Existence. Many but not all functions have Laplace transforms.
Theorem 5.2.1. If is defined for , piecewise continuous, and is exponential of order (satisfies for some constant and constant the inequality for all ), then the Laplace transform exists for all .
Text Example 5.9. Solve with initial conditions and .
Text Example 5.8. Solve with initial conditions and .