Lecture 4 Notes

4 3 5 1 i 2 2 3 4 2 1 i 1 1i 1 2 3 4 complex

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Unformatted text preview: resented as f ￿￿ (x0 ) ￿ 2 f (x) = f (x0 ) + f (x0 )(x − x0 ) + (x − x0 ) + · · · 2! x2 x3 + + ··· • What function has Taylor series 1 + x + 2! 3! (A) cos x (C) ex (B) sin x (D) ln x Complex number review • Use Taylor series to rewrite cos θ + i sin θ . x3 x5 sin x = x − + − ··· 3! 5! 2 4 x x cos x = 1 − + − ··· 2! 4! Complex number review • Use Taylor series to rewrite cos θ + i sin θ . cos θ + i sin θ x3 x5 sin x = x − + − ··· 3! 5! 2 4 x x cos x = 1 − + − ··· 2! 4! Complex number review • Use Taylor series to rewrite cos θ + i sin θ . θ2 θ4 cos θ + i sin θ = 1 − + − ··· 2! 4! x3 x5 sin x = x − + − ··· 3! 5! 2 4 x x cos x = 1 − + − ··· 2! 4! Complex number review • Use Taylor series to rewrite 2 cos θ + i sin θ . 4 ￿ 3 5 2 4 θ θ θ θ cos θ + i sin θ = 1 − + − · · · +i θ − + − ··· 2! 4! 3! 5! x3 x5 sin x = x − + − ··· 3! 5! x x cos x = 1 − + − ··· 2! 4! ￿ Complex number review • Use Taylor series to rewrite 2 cos θ + i sin θ . 4 ￿ 3 5 θ θ θ θ cos θ + i sin θ = 1 − + − · · · +i θ − + − ··· 2! 4! 3! 5! ￿ θ2 θ3 θ4 2 = 1 + iθ + (−1) + (−1)i + (−1) + ··· 2! 3! 4! Complex number review • Use Taylor series to rewrite 2 cos θ + i sin θ . 4 ￿ 3 5 θ θ θ θ cos θ + i sin θ = 1 − + − · · · +i θ − + − ··· 2! 4! 3! 5! ￿ θ2 θ3 θ4 2 = 1 + iθ + (−1) + (−1)i + (−1) + ··· 2! 3! 4! Complex number review • Use Taylor series to rewrite 2 cos θ + i sin θ . 4 ￿ 3 5 θ θ θ θ cos θ + i sin θ = 1 ...
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This note was uploaded on 02/12/2014 for the course MATH 256 taught by Professor Ericcytrynbaum during the Spring '13 term at UBC.

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