2130_Chapter7_Notes

xn fundamental matrix t x1 xn x11

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Unformatted text preview: . −2 + (1 − i)(1 + i) 0 9 / 10 5 Exa 2 (slide 3) λ = 2 + i, v = 1 1+i =⇒ veλt = 1 e(2+i)t 1+i = 1 cos t + i sin t e2t (cos t + i sin t) = e2t 1+i (1 + i)(cos t + i sin t) = cos t + i sin t e2t cos t − sin t + i(cos t + sin t) = sin t cos t e2t e2t +i cos t + sin t cos t − sin t x(1) x(2) General solution: x = c1 cos t sin t e2t + c2 e2t . cos t − sin t cos t + sin t 10 / 10 6 APMA 2130 Section 7.7: Fundamental Matrices Post-Lecture Handout Dr. Bernard Fulgham University of Virginia July 22, 2013 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 General Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Special Matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Example...
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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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