SampleFinalExam - Engineering 6 Sample Final Exam(with...

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Engineering 6 Sample Final Exam (with solutions) University of California, Davis Note: This sample final exam is just that: a sample. It is not a comprehensive review of the material. See the midterm and final exam study guides for the complete list of topics that may be covered. Note: When you are asked to solve a problem, you are to first develop a mathematical algorithm, then write a Matlab script to compute and display the specified values. You must first show your work in developing the algorithm, either mathematically or in script comments. All computation is to be done in the script, not in your head or by calculator. Matlab variable names should correspond to the chosen mathematical variables. Comments must be included in the script to define variables and to explain sections of the code. The output displayed by the script should clearly identify the variable whose value is displayed and specify its units. 1. (12 points) Evaluate the following Matlab expressions, giving the format short display of the results (not necessary to add the "ans =" line). (a) –5^2 (b) log10(100) – log10(0.01) (c) conj(1 – j*3) (d) (180/pi)*angle(j) (e) norm( [3 4] ) (f) (2:3:15) (g) linspace(0, 1, 6) (h) [1 2; 5 7]' 2. (8 points) In the following sequence of Matlab commands and displayed output, an expression involving polynomials has been transformed from one form to another. Write the mathematical form of the polynomial expressions defined at the beginning and at the end of the sequence of commands. » n = [2 11 24 25];
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» d = [1 4 5]; » [c,r,q] = residue(n,d) c = 1.0000 - 3.0000i 1.0000 + 3.0000i r = -2.0000 + 1.0000i -2.0000 - 1.0000i q = 2 3 3. (8 points) Write a script to solve the following matrix equation for the matrix C A ( CB + A ) = B where A ° ± ² ³ ´ µ - = 4 2 9 3 and B ° ± ² ³ ´ µ - = 9 7 3 2 4. (8 points) Write a script to plot the combined mesh/contour plot (using meshc) for the function: ] ) [( 2 2 2 ) , ( y y x xe y x f x + - = = Plot the ranges –2 ° x ° 2 and –2 ° y ° 2 with a spacing of 0.1.
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