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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH314, Modeling Realizable Phenomena HW 1 Gidon Eshel, Physics Department, Bard College Annandale-on-Hudson, NY 12504-5000, x-7232, geshel@bard.edu . 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 ¯
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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 ve cases, order 0, orders 0 and 1, orders 02 and orders 03 (for a total of 20 approximations). (5) Linearize about ( x, y ) dx dt = xy + x 2 dy dt = xy 2-y 2 cos( x ) where all Greek letters denote constant coecients, and Roman letters denote variables. 1...
View Full Document

Ask a homework question - tutors are online