notes 6-1 - SECTION 6.1 THE LAPLACE TRANSFORM The Laplace...

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Unformatted text preview: SECTION 6.1 THE LAPLACE TRANSFORM The Laplace transform is a particularly useful example of a general process in mathemat- ics, namely, transform a problem from a difficult setting like calculus into a simpler setting like algebra, solve the transformed problem, and transform the answer back to the difficult setting. In this case, the Laplace transform L • turns differential equation problems into algebraic problems, • includes initial values automatically, in fact, works only when initial values are given, • solves nonhomogeneous differential equations nearly automatically, and • handles nonhomogeneous differential equations in which the right-hand-side is discon- tinuous. EXAMPLES. (1) Hang a chunk of iron from a spring fastened to the ceiling. Start it vibrating. Let it vibrate for 12 seconds. Now turn on a weak magnet underneath the chunk for 25 seconds. Then turn the magnet off....
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This note was uploaded on 11/28/2010 for the course M 56840 taught by Professor Schurle during the Spring '10 term at University of Texas at Austin.

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notes 6-1 - SECTION 6.1 THE LAPLACE TRANSFORM The Laplace...

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