MATH201 Lecture 16: 16. Solving Equations using Laplace Transform.pdf

• School: University of Alberta
• Department: Mathematics
• Course: MATH201
• Professor: van

Document Summary

Feb. 13, 2012: many examples here are taken from the textbook. The rst number in () refers to the problem number in the ua custom edition, the second number in () refers to the problem number in the 8th edition. Given: review a y + b y + c y = f (t) with y(0), y (0), transform the equation, transform the right hand side, transform the left hand side. F (s) = l{f }(s). (1) (2) (3) (4) and substitute into the equations: solve for y , compute y = l 1{y }, partial fractions, factorize q, write. L{y } = s2 y s y(0) y (0); Q = (s r1)m1(cid:10) (s rk)mk [(s 1)2 + 1. A11 + a12 (s r1) +(cid:10) + a1m1 (s r1)m1 1. Ak1 + ak2 (s rk) +(cid:10) + akmk (s rk)mk 1. Cl nl (s l) + dl nl l. Cl1 (s l) + dl 1 l.