ENG006 MT1 F09 Key Lagerstrom

# ENG006 MT1 F09 Key Lagerstrom - Engineering 6 Midterm...

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Engineering 6 Midterm Solutions, Fall 2009 Regrade requests must be submitted in writing to Dr. Lagerstrom no later than the Review/Q&A session on Wednesday, November 18. Regrades will only be considered in cases where it looks like the grader missed something. That is, requests along the lines of "I think I deserve more points" will not get very far, because the the grading scale on each problem was applied consistently for all students. Note also : Your exam may have been photocopied before it was returned, so please don't risk your engineering career here at UCD by changing an answer and submitting it for a regrade. Exam Version A (blue and white copies) Problem 1 (22 points). (a) (6 points) x = linspace(-2,39,873); %Define values of x in row vector a = [7 0 13 -9 16]; %Define polynomial coefficient vector A = polyval(a,x); %Calculate values (b) (6 points) x = linspace(-2,39,873); %Okay to leave this out if have it in part (a) A = 7*x.^4 + 13*x.^2 – 9*x + 16; %Note: only two dot operators needed. (c) (8 points) h = [2 0 0 3 0 0 0 -8]; %Define polynomial coefficient vectors g = [12 5 4 15]; [c r q] = residue(h,g); %Get residues (c), roots (r), and quotient coeffs (q) Note: Okay to write [c,r,q] = etc. The ratio H/G is an improper rational function, so the general form of the result will be (assuming no repeated roots) n n r x c r x c r x c x Q x G x H 2 2 1 1 ) ( ) ( ) ( where Q(x) is the quotient polynomial and the rest of the terms are the partial fraction expansion. In the Matlab code, the variable q will contain the coefficients of Q(x), the variable c will contain the c’s (residues), and the variable r will contain the r’s (roots of the denominator polynomial G(x)). (d) (2 points) There would be 3 terms in the partial fraction expansion, because the denominator polynomial G(x) is third order, and thus has three roots.

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