xiii Note to the reader: This is a customized book for Old Dominion ...

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ORDINARY DIFFERENTIAL EQUATIONS 511Physical problemsChapter 08.00A Physical problem - general engineering 511Chapter 08.00B Physical problem - chemical engineeringChapter 08.00C Physical problem - civil engineering 515Chapter 08.00D Physical problem - computer engineeringChapter 08.00E Physical problem - electrical engineeringChapter 08.00F Physical problem – industrial engineeringChapter 08.00G Physical problem - mechanical engineering 517Chapter 08.01 Primer for ordinary differential equations (View it on web)Go to http://numericalmethods.eng.usf.edu>Keyword> Primer on ordinary differential equationsMultiple-choice test 523Problem set 525Chapter 08.02 Euler’s method for ordinary differential equations 527What is Euler’s method? 527Derivation of Euler’s method 528Multiple-choice test 536Problem set 539Chapter 08.03 Runge-Kutta 2nd order method 543What is the Runge-Kutta 2nd order method? 543Heun’s method 546Midpoint method 546Ralston’s method 547How do these three methods compare with results obtained if we found f x,ydirectly? 550How do we get the 2nd order Runge-Kutta method equations? 551Multiple-choice test 554Problem set 557Chapter 08.04 Runge-Kutta 4th order methodWhat is the Runge-Kutta 4th order method?How does one write a first order differential equation in the above form?Multiple-choice testProblem setChapter 08.05 On Solving higher order equations 561Problem set 570Chapter 08.07 Finite difference method 572What is the finite difference method? 572Multiple-choice test 586Problem set 590xxiv
FAST FOURIER TRANSFORM 593Physical ProblemsChapter 11.00C Physical problem – civil engineering 593Chapter 11.01 Introduction to Fourier series 606Chapter 11.02 Continuous Fourier series 611Derivation of formulas for a 0 , a k , and b k 611A FORTRAN program for finding Fourier coefficients a 0 , a k , and b k 612Multiple-choice test 621Chapter 11.03 Fourier transform pair: frequency and time domain 624Representation of a complex number in polar coordinates 629Important notes 630Non-periodic function 632Multiple-choice test 635Chapter 11.04 Discrete Fourier transform 637Derivations of DFT Formulas 637Detailed explanation about aliasing phenomenon, Nyquist samples, Nyquist rate 641Multiple-choice test 646Chapter 11.05 Informal development of Fast Fourier Transform (FFT) 648Factorized matrix and further operation count 650Companion node observation 655Companion node spacing 655Companion node computation 655Determination of W P 656Computer implementation to find value of “P” (in W P ) 657Multiple-choice test 666Chapter 11.06 Theoretical Development of FFT 669FFT algorithms for N = 2 r 669Consider the case N = 2 r = 2 3 = 8 671Consider the general case N = 2 r (r = any integer number) 673FFT algorithms for N = r 1 r 2 (where r 1 , r 2 are integers) 675General FFT algorithms and relationships between FFT for N = 2N = r 1 r 2 r 3 = (2)(2)(2) = 8 679Twiddle factor FFT algorithms for N = (r 1 = 4) (r 2 = 4) = 16 681Multiple-choice test 684(r = 3)=8 versusIndex 688Answers to Selected Problems 694xxv
Page 1 and 2: TABLE OF CONTENTSNote to the reader
Page 3 and 4: NONLINEAR EQUATIONS 112Physical pro
Page 5 and 6: What do you mean by the rank of a s
Page 7 and 8: On-line chess-like game for reorder
Page 9 and 10: REGRESSION 339Physical problemsChap
Page 11: Problem setChapter 07.07 Integratin

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