week9 - ))-( n +1) ) These formulas can be deduced from the...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Week 9 Material to be covered: 6.3, 6.4 Homework to be handed Nov. 2 Section 6.4: 1,2,3 (Draw the graphs at least half a page large) Section 3.7: 7, 17 Section 2.3: 13, 19 Find the general solution of y (4) - 4 y (2) + 4 y = te 2 t . , Two interesting Laplace transforms not discussed in the book are L [ t n e at cos( bt )]( s ) = n ! 2 ( (( s - ( a + ıb )) - ( n +1) + ( s - ( a - ıb )) - ( n +1) ) L [ t n e at sin( bt )]( s ) = n ! 2 ı ( ( s - ( a + ıb )) - ( n +1) - ( s - ( a - ıb
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ))-( n +1) ) These formulas can be deduced from the formulas for L [ t n e at ] using Eulers formula. These Laplace transforms appear in the study of resonances of higher order equations. When you get these Laplace transforms it is algebraically simple to use partial fractions using complex roots. 1...
View Full Document

This note was uploaded on 02/01/2011 for the course MATH 427K taught by Professor Delallave during the Spring '11 term at University of Texas at Austin.

Ask a homework question - tutors are online