Question Description
You will do areview on similarities and differences between Calculus of Real and Complex numbers. Themain goal of this project is to observe the main differences of calculus of complex numbers in C over thereal numbers and what advantages this differences brings to other fields of mathematics and to science.
OBJECTIVE: The aim of this objective is to compare the set of complex numbers and the set of realnumbers from algebraic structural and from geometric perspective (such as closedness,nth-roots, ’rational’ powers, infinity as extending the number system, roots of polynomials,…).
!!! Write a report on Objective, about 5 − 6 pages with proper citations, and on a separatepage(s) the references (only the ones used in the report), in an MS Word file.
You can use the following classical books [PS06], [GK06], [Rud87], [CB84], [MH87], [Ahl78],[Lan99], [Nee97].
REFERENCES
[Ahl78] Lars V. Ahlfors, Complex analysis, third ed., McGraw-Hill Book Co., New York, 1978, An introduction tothe theory of analytic functions of one complex variable, International Series in Pure and Applied Mathematics.MR 510197
[CB84] Ruel V. Churchill and James Ward and Brown, Complex variables and applications, fourth ed., McGraw-HillBook Co., New York, 1984. MR 730937
[GK06] Robert E. Greene and Steven G. Krantz, Function theory of one complex variable, third ed., Graduate Studiesin Mathematics, vol. 40, American Mathematical Society, Providence, RI, 2006.
[Lan99] Serge Lang, Complex analysis, fourth ed., Graduate Texts in Mathematics, vol. 103, Springer-Verlag, NewYork, 1999. MR 1659317[MH87] Jerrold E. Marsden and Michael J. Hoffman, Basic complex analysis, second ed., W. H. Freeman and Company,New York, 1987. MR 913736
[Nee97] Tristan Needham, Visual complex analysis, The Clarendon Press, Oxford University Press, New York, 1997.MR 1446490
[PS06] S. Ponnusamy and Herb Silverman, Complex variables with applications, Birkhauser Boston, Inc., Boston, ¨MA, 2006.
[Rud87] Walter Rudin, Real and complex analysis, third ed., McGraw-Hill Book Co., New York, 1987.
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