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Chapter7Laplace Transforms

The Laplace transform is an integral transform that can be used to solve IVPs. Just as with all other solution methods for higher--order, linear, differential equations, the Laplace transform method reduces the problem to an algebraic one, typically a partial fractions decomposition problem.

Unfortunately, the Laplace transform method typically requires more work, or computation than the previous methods of undetermined coefficients and variation of parameters. But the Laplace method is more powerful. It will allow us to solve equations with more complicated forcing functions than before. It is especially useful for analyzing electric circuits where the power is periodically switched on and off.