This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 righthandside 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....
View
Full
Document
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.
 Spring '10
 SCHURLE

Click to edit the document details