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Chapter 14: Q22P (page 687)
Find the residues of the following functions at the indicated points. Try to select the easiest of the methods outlined above. Check your results by computer.
Hence, the residue of the function at is -1 .
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A fluid flow is called irrotational if 鈭嚸梀 = 0 where V = velocity of fluid (Chapter 6, Section 11); then V = 鈭囄�. Use Problem 10.15 of Chapter 6 to show that if the fluid is incompressible, the 桅 satisfies Laplace鈥檚 equation. (Caution: In Chapter 6, we used V = v蟻, with v = velocity; here V = velocity.)
Using the definition (2.1) of show that the following familiar formulas hold.
Find the residues of the following functions at the indicated points. Try to select the easiest of the methods outlined above. Check your results by computer.
Question: Use the Cauchy-Riemann conditions to find out whether the functions in Problems 1.1 to 1.21 are analytic.
Find the residues of the following functions at the indicated points. Try to select the easiest of the methods outlined above. Check your results by computer.
at
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