2130_Chapter7_Notes

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Unformatted text preview: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exa 2 (slide 3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matrix Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 3 4 5 6 7 8 9 Introduction System of n first order ordinary differential equations: x′ = F1 (t, x1 , x2 , . . . , xn ), 1 x′ = F2 (t, x1 , x2 , . . . , xn ), 2 . . . ′ = F (t, x , x , . . . , x ), xn n 12 n where each xk is a function of t. If each Fk is a linear function of x1 , . . . , xn , then the system of equations is linear; otherwise, it is nonlinear. Systems of higher order differential equations can similarly be defined. 2/9 Linear Systems Linear system of equations: x′ = p11 (t)x1 + p12 (t)x2 + · · · + p1n (t)xn + g1 (t), 1 x′ = p21 (t)x1 + p22 (t)x2 + · ·...
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This note was uploaded on 03/19/2014 for the course APMA 2130 taught by Professor Bernardfulgham during the Fall '09 term at UVA.

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