2130_Chapter7_Notes

If x1 xn are solutions then c1 x1 cn

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Unformatted text preview: . . . . . . . . . . . . . . Initial Value Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Homogeneous System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 3 4 5 Introduction System of n linear 1st order equations: x′ = p11 (t)x1 + p12 (t)x2 + · · · + p1n (t)xn + g1 (t), 1 x′ = p21 (t)x1 + p22 (t)x2 + · · · + p2n (t)xn + g2 (t), 2 . . . x′ = pn1 (t)x1 + pn2 (t)x2 + · · · + pnn (t)xn + gn (t). n Equivalent to x′ = P(t)x + g(t) : ′ x1 g1 (t) p11 (t) · · · p1n (t) x1 . . . . + . . .. . . . . = . . . . . . . ′ gn (t) pn1 (t) · · · pnn (t) xn xn x′ P(t) x g(t) 2 / ?? Initial Value Problem Theorem 7.1.2 If the functions P(t) and g(t) are continuous on a...
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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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