CHEN 4601 Lecture Notes - Lecture 9: Stamen, Theeb
24 Sep 2015
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1st exam --> oct 5 --> oct 7. If the roots are on left of im axis, convergence. On right, divergence on the imaginary axis, including 0 point sustained. Last piece of general background: solution of systems of 1st order odes using lt (before, we just focused on single eqns, input/output representation of a linear system using l. t. When we have a system of odes ex: take lt of each eqn gather all unknowns on same side solve by substitution, cramer"s rule, then invert x1 and x2 from function of s to function of t. This approach generalizes to n equations this can be written more compactly as. Take lt of both sides as before multiply by identity matrix b/c s = scalar and a = matrix terms due to initial conditions --> superimposed term due to forcing inputs. Remark 1: inversion of a matrix (not inverting the matrix itself) of l. t. is done element by element.
