144. exercises Upper bounds for moduli of complex Integrals

#bsmaths #mscmaths #complexanalysis #complexintegral Upper bounds for moduli of complex Integrals Q.1

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Course Contents:
The Concept of Analytic Functions
• Complex numbers, complex planes, complex functions
• Analytic functions
• Entire functions
• Harmonic functions
• Elementary functions: complex exponential, logarithmic and hyperbolic functions
Infinite Series
• Power series, derived series, radius of convergence
• Taylor series and Laurent series
Conformal Representation
• Transformation, conformal transformation
• Linear transformation
• Möbius transformations
Complex Integration
• Complex integrals
• Cauchy-Goursat theorem
• Cauchy’s integral formula and their consequences
• Liouville’s theorem
• Morera’s theorem
• Derivative of an analytic function
Recommended Books:
1. D. G. Zill and P. D. Shanahan, Complex Analysis, (Jones and Bartlett Publishers,
2003)
2. H. S. Kasana, Complex Variables: Theory and Applications, (Prentice Hall, 2005)
3. J. W. Brown and R. V. Churchill, Complex Variables and Applications, 7th edition,
(McGraw Hill Company, 2004)
4. M. R. Spiegel, Complex Variables, (McGraw Hill Book Company, 1974)
5. Louis L. Pennisi, Elements of Complex Variables, (Holt, Linehart and Winston, 1976)
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