CH-03 (523171), страница 5
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Apply plot.m of MATLAB to obtain a plot of P(x) = x6 + x5–8x4 + 14x3+ 13x2–111x + 90 = 0 vs. x for –4≤x≤3 as shown below.© 2001 by CRC Press LLC3. Find the roots of P(x) = x6 + x5–8x4 + 14x3 + 13x2–111x + 90 = 0 byapplication of the program Bairstow. Are the real roots graphically verified in the plot shown in Problem 2?4. Apply root.m of MATLAB to find the roots of P(x) = x6 + x5–8x4 + 14x3+ 13x2 111x + 90 = 0.5. Apply the program Bairstow to solve the characteristic equations derivedby the program CharacEq: (1) 3–15 2–18 = 0, (2) 3–182 + 109–222 = 0, and (3) 3–122 + 47 –60 = 0.6. Apply the program Bairstow to solve for the characteristic equationsderived for the program EigenODE.Stb:λ2 − 36λ + 243 = 0,λ3 − 96λ2 − 2560λ − 16384 = 0,λ4 − 200λ3 + 13125λ2 − 312500λ + 1953125 = 0,andλ5 − 360λ4 + 466563 − 2612736λ2 + 5.878656x10 7 λ − 3.62791x108 = 07.
Apply roots.m of MATLAB to find the roots of the polynomials givenin Problem 5 and then graphically verify the locations of these roots byplotting the polynomial curves using plot.m.8. Repeat Problem 7 except for those polynomials given in Problem 6.9. Apply NSolve of Mathematica to solve Problems 2 to 6.3.6 REFERENCES1. M. Abramowitz and I. A. Stegun, editors, “Handbook of Mathematical Functionswith Formulas, Graphs, and Mathematical Tables,” Applied Mathematics Series 55,National Bureau of Standards, Washington, DC, 1964.2. Y.
C. Pao, Elements of Computer-Aided Design and Manufacturing, CAD/CAM, JohnWiley & Sons, New York, 1984.3. A. Higdon, E. H. Ohlsen, W. B. Stiles, J. A. Weese, and W. F. Riley, Mechanics ofMaterials, John Wiley & Sons, New York, Fourth Edition, 1985.4. J. F. Traub, Iterative Methods for Solution of Equation, Prentice-Hall, EnglewoodCliffs, NJ, 1964.5. A. E. Taylor, Advanced Calculus, Ginn & Co., Boston, 1955.6. W. H. Li, Fluid Mechanics in Water Resources Engineering, Allyn & Bacon, Boston,1983.7. C.
R. Wylie, Jr., Advanced Engineering Mathematics, McGraw-Hill, New York, 1960.© 2001 by CRC Press LLC.
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