Download Advanced Engineering Mathematics with MATLAB, Second Edition by Dean G. Duffy PDF

By Dean G. Duffy

You could study loads of arithmetic during this publication yet not anything approximately MATLAB. there is not any strong perform during this publication. a touch for the writer. try and make a CD-ROM with all examples on it. So everybody can get acquainted with MATLAB and the skin. top will be to double or triple the variety of examples. (good examples in MATLAB Code) reconsider it and that i may be the first who buys the enhanced version of this e-book or you in simple terms need to swap the name in :Advanced Engineering arithmetic photographs by means of MATLAB. thank you for studying.

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Additional resources for Advanced Engineering Mathematics with MATLAB, Second Edition

Example text

If the singularity were not inside the contour, then the integrand would have been analytic inside and on the contour C. In this case, the answer would then be zero by the Cauchy-Goursat theorem. Kef ki , 1984: The Cauchy Method of Residues: Theory and Applications. Reidel Publishing, 361 pp. 3 gives the historical development of the residue theorem.

F(z)=z3 sin2(z); z0=0 46 Advanced Engineering Mathematics with MATLAB 5. 6. 7. 8. 9. 10. 8 THEORY OF RESIDUES Having shown that around any singularity we may construct a Laurent expansion, we now use this result in the integration of closed complex integrals. Consider a closed contour in which the function f(z) has a number of isolated singularities. As we did in the case of Cauchy’s integral formula, we introduce a new contour C which excludes all of the singularities because they are isolated.

The result of a line integral is a complex number or expression. Unlike its counterpart in real variables, there is no physical interpretation for this quantity, such as area under a curve. Generally, integration in the complex plane is an intermediate process with a physically realizable quantity occurring only after we take its real or imaginary part. For example, in potential fluid flow, the lift and drag are found by taking the real and imaginary part of a complex integral, respectively. How do we compute C f(z) dz?

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