practiceExam1Sample2

practiceExam1Sample2 - Problem 1: [8 points] If possible,...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Problem 1 : [8 points] If possible, rewrite the systems of simultaneous equations defined by in a matrix-vector form that could be solved using Gauss elimination. If this task is not possible, state why. (a) 32 7 12 2 12 2 x yx yy zx y xz y += +− =− + (b) 13 4 31 4 4 21 7 2 22 xx x x x + −= = = 0 0 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Problem 2 : [8 points] For each of the ODEs defined below, calculate by finding the ODE’s exact solution. (1) y (a) 2 x dy x e dx π =+ with . (0) 0 y = (b) with 33 1 8 yy y ′′ −− = 0 (0) 0 y = and (0) 1 y = . 2
Background image of page 2
Problem 3 : [7 points] This problem considers the Taylor series expansion of the function 2 () x f xe = . (a) Differentiate () f x to find () f x and f x ′′ . (b) Use the results from (a) to approximate using a second order Taylor expansion expanded around x = 0. State the error between your calculated result and the exact value of to 3 significant figures. (0.2) f (0.2) f (c) Repeat part(b) using a Taylor series expanded around x = 0.4.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 8

practiceExam1Sample2 - Problem 1: [8 points] If possible,...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online