MATH201 Lecture Notes - Lecture 15: Partial Fraction Decomposition, Horse Length, Gaussian Elimination

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

Document Summary

Feb. 10, 2012: many examples here are taken from the textbook. F (s) = l{f }(s): transform the left hand side: denote y (s) = l{y}(s). L{y } = s2 y s y(0) y (0); L{y } = s y y(0) and substitute into the equations: the transformed equation is then (a s2 + b s + c) y = f (s) + a s y(0) + a y (0) + b y(0). Solve for y (s): take inverse transform of y (s) to get y. That is nd y(t) such that l{y} = y : most useful inverses: 1 (s a)n+1(cid:27) = eat tn n! (1) (2) (3) (4) (5) (6) (7) (8) (9) (10: quiz: calculate. L 1(cid:26) a (s ) + b s s + 5. L 1(cid:26) (s )2 + 2 (cid:27) = e t [a cos t + b sin t].