e6exam1secAsolnsF06

e6exam1secAsolnsF06 - Engineering 6 Fall 2006 Midterm...

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Unformatted text preview: Engineering 6, Fall 2006 Midterm Solutions Lecture Section A (MWF9-10) Regrade requests: Regrade requests must be submitted in writing to Dr. Lagerstrom no later than the lecture section on Monday, November 20. 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 green copies) Problem 1. (24 points total; 6 points each part) Give a brief explanation of what the following lines of Matlab code do, making sure to include the meaning of the variables and how each pair of examples is different. (a) [a b] = residue(f,g) [a b c] = residue(f,g) Answer: The residue function calculates the partial fraction expansion of a polynomial ratio F(x)/G(x), where f and g are the coefficient vectors of F and G. The first line calculates the expansion when F/G is a proper rational function, i.e., the order of F is less than the order of G, and the variable "a" is a row vector containing the residues of the expansion and the variable "b" is a row vector containing the roots of G(x). The second line calculates the expansion when F/G is an improper rational function, i.e., the order of F is greater than or equal to the order of G. In this case F/G can be written as Q(x) + R(x)/G(x), where the Matlab code yields "c" as the coefficient vector of the polynomial Q, and "a" and "b" are the residues and roots, respectively, of the partial fraction expansion of the remainder term R/G. (b) a = polyder(c,d) [a b] = polyder(c,d) Answer: In the first line, "c" and "d" are variables representing the coefficient vectors of two polynomials, and the polyder function multiplies the two polynomials and then takes the derivative of the result, storing the coefficients of the result in "a". The second line is similar, except that the polyder function divides the two polynomials and then takes the derivative of the result, storing the coefficients of the numerator of the result in "a" and the coefficients of the denominator of the result in "b". (c) a = conv(c,d) [a b] = deconv(c,d) Answer: In the first line, "c" and "d" are variables representing the coefficient vectors of two polynomials, and the conv function multiplies the two polynomials and stores the coefficients of the polynomial result in "a". In the second line, "c" and "d" are the same, except the deconv function divides the two polynomials and stores the the coefficients of the numerator of the result in "a" and the coefficients of the denominator of the result in "b"....
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This note was uploaded on 01/22/2011 for the course ENG 006 taught by Professor Lagerstrom during the Fall '06 term at UC Davis.

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e6exam1secAsolnsF06 - Engineering 6 Fall 2006 Midterm...

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