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AMS361-Lecture-11-15-2011-Laplace-Trans

# AMS361-Lecture-11-15-2011-Laplace-Trans - AMS 361 Calculus...

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1 AMS 361: Calculus IV Fall 2011 Lecture 11-15-2011 Linear System of DEs & Laplace Transforms Goals for Tuesday (11/15/2011) lecture: Understanding the solutions of the following systems of DEs: Example 2 ࠵? ! ࠵? ! ! = 4 3 3 4 ࠵? ! ࠵? ! This example will show that the system has complex eigenvalues ࠵? ! = 4 + ࠵? 3 ࠵? ! = 4 ࠵? 3 and we can find the associated eigenvectors for the two eigenvalues. Example 3 ࠵? ! ࠵? ! ! = 4 3 3 4 ࠵? ! ࠵? ! This example will show that the system has complex eigenvalues ࠵? ! = 4 = ࠵? !

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2 and we can find the associated eigenvector ࠵? ! for the eigenvalue ࠵? ! . We have to compose the linearly independent solution by introducing ࠵? ! = ࠵? ! ࠵? + ࠵? ! ࠵? !" Example 4 ࠵? ! ࠵? ! ! = 3 2 7 5 ࠵? ! ࠵? ! + 3 2 ࠵? Example 5 Two coupling blocks by two massless springs on smooth horizontal bench. Now, please enjoy class video by following instructions below: Step 1: Go to URL: http://docs.google.com/ Step 2: Login as Password: wow361wow Step 3: Click on the only video file and sit back and enjoy the lecture. Please email me if you have any questions and comments