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HW2 - x = 5(4 Use the above expansion to approximate(a at x...

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MATH314, Modeling Realizable Phenomena HW 1 Gidon Eshel, Physics Department, Bard College Annandale-on-Hudson, NY 12504-5000, x-7232, [email protected] . Due Thursday 9/23/2010, in hard copy, succinct, typed and neatly printed form. (1) Which of the following (with Greek letters denoting numerical constants) is linear? (a) α sin( x ) (b) β x (c) γ x 2 (d) ( δx ) ln( x ) (e) η/x (2) Expand symbolically the function (a) above in a Taylor series about ¯ x , including ex- plicitly orders 0–3. (3) Write down explicitly the above expansion around ¯
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Unformatted text preview: x = 5. (4) Use the above expansion to approximate (a) at x = 4 . 8 , 4 . 9 , 5 , 5 . 1 , 5 . 2 using, in each of the above ﬁve cases, order 0, orders 0 and 1, orders 0–2 and orders 0–3 (for a total of 20 approximations). (5) Linearize about (¯ x, ¯ y ) dx dt = αxy + βx 2 dy dt = γxy 2-δy 2 cos( x ) where all Greek letters denote constant coeﬃcients, and Roman letters denote variables. 1...
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