MATH 355 Lecture 6: Functions of Matrices Math 410
16 Mar 2016
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Linear equations with constant coefficients for matrices: to find a solution with a different initial condition. Remark: if we need to solve a vector equation. Inhomogeneous systems: the above is only if you have the actual initial condition, the below is the more general case (if you have a condition not at t=0) Example: how do you go from a general system to an n-th order differential equation, note: in above, the a matrix, the bottom right the term is actually (a(n-1)) Example: fundamental solution of homogenous system, notes, if b>0 then stable, if b=0 then neutral (stable), oscillations but no damping, solution will oscillate without approaching zero. Now lets look at the nonhomogenous system of the same example: how does the forcing affect the system, extra credit due friday!!! : what is the something else above: find the qualitative difference between when w =/= sqrt() above and when w=sqrt( ) above.
