#bsmaths #mscmaths #complexanalysis #complexintegral<br />Q. 3 exercises Section (40) Contour Integration<br />%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<br />Course Contents:<br />The Concept of Analytic Functions<br />• Complex numbers, complex planes, complex functions<br />• Analytic functions<br />• Entire functions<br />• Harmonic functions<br />• Elementary functions: complex exponential, logarithmic and hyperbolic functions<br />Infinite Series<br />• Power series, derived series, radius of convergence<br />• Taylor series and Laurent series<br />Conformal Representation<br />• Transformation, conformal transformation<br />• Linear transformation<br />• Möbius transformations<br />Complex Integration<br />• Complex integrals<br />• Cauchy-Goursat theorem<br />• Cauchy’s integral formula and their consequences<br />• Liouville’s theorem<br />• Morera’s theorem<br />• Derivative of an analytic function<br />Recommended Books:<br />1. D. G. Zill and P. D. Shanahan, Complex Analysis, (Jones and Bartlett Publishers,<br />2003)<br />2. H. S. Kasana, Complex Variables: Theory and Applications, (Prentice Hall, 2005)<br />3. J. W. Brown and R. V. Churchill, Complex Variables and Applications, 7th edition,<br />(McGraw Hill Company, 2004)<br />4. M. R. Spiegel, Complex Variables, (McGraw Hill Book Company, 1974)<br />5. Louis L. Pennisi, Elements of Complex Variables, (Holt, Linehart and Winston, 1976)<br />...<br /><a href="https://www.youtube.com/watch?v=0OprD5_JCVE" target="_blank" rel="nofollow">https://www.youtube.com/watch?v=0OprD5_JCVE</a>