MATH201 Lecture Notes - Lecture 19: Dirac Delta Function, Integral Equation, Step Function

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

Document Summary

Feb. 27, 2012: many examples here are taken from the textbook. L(cid:8)y(n)(cid:9) = sn y sn 1 y(0) sn 2 y (0) (cid:10) y(n 1)(0). L{y } = s2 y s y(0) y (0); L{y } = s y y(0); in general (1) (2) (3: simple variable coe cient: use. L{tn f (t)} = ( 1)n dn dsn f (s) combined with the above formulas: integral equation: check if the integral is a convolution f g = r 0 so use t f (t v) g(v) dv. L{f g } = f (s) g(s): right hand side, table, properties: L{eat f (t)} = f (t a); L{tn f (t)} = ( 1)n dn dsn f (s): if f (t) has jumps, represent using unit step function, then use. L{g(t) u(t a)} = e as l{g(t + a)}: if f (t) is periodic with period t , then. L{f } = r 0 e st f (t) dt.