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# week9 - n 1 These formulas can be deduced from the formulas...

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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
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Unformatted text preview: ))-( n +1) ) These formulas can be deduced from the formulas for L [ t n e at ] using Euler’s 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...
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