MATH 251 Lecture Notes - Polynomial Long Division, Partial Fraction Decomposition, Junkers J 1
Document Summary
Partial fraction decomposition for inverse laplace trans- form. We, however, never have to do this polynomial long division, when partial fraction. Decomposition is applied to problems from chapter 6. Another important fact in chapter 6 is that we use only the following three types of fractions: 1. s a (s a)2 + b2 , 2. (s a)2 + b2 , 3. (s a)n , b. 1 because we know the corresponding inverse laplace transforms s a. 3. l 1(cid:20) 1 (s a)4(cid:21) = (s a)2 + b2(cid:21) = eat cos(bt), 2. l 1(cid:20) s a(cid:21) = eat, l 1(cid:20) eat, l 1(cid:20) (s a)2(cid:21) = teat, l 1(cid:20) (s a)5(cid:21) = eat, . 2 (s a)3(cid:21) = (s a)n+1(cid:21) = We will call fractions 1,2,3 as standard fractions. The partial fraction decomposition for inverse laplace transform is as follows. b (s a)2 + b2(cid:21) = eat sin(bt), (1) (2)
