Course Description
Complex numbers, Cartesian and polar representation of complex numbers, powers and roots of complex numbers. Limits and continuity of a complex function. Analytic functions, Cauchy-Riemann equations, harmonic functions. Exponential, trigonometric, hyperbolic functions and logarithmic functions. Complex integration, contour integrals, Cauchy's theorem, Cauchy's formula. Series representation of analytic functions, Taylor and Laurent series, Zeros and singularities. Residue theory. Applications to real and improper integrals. The conformal mappings.
Course Objectives & Outcomes
The objectives of this course are to:
- introduce students to the Complex Number System
- equip students with necessary knowledge and skills to enable them handle mathematical operations,analyses and problems involving complex numbers.
Upon successful completion of this course, the student will be able to:
- Solve problems of limits, continuity, differentiation, and integration of functions of complex variables.
- Represent analytic functions using Taylor and Laurent series.
- Use of the Residue theorem in solving improper integrals.
- Use of the conformal mappings in solving problems.
- Draw regions, domains and complex functions in complex plane.
References
1. Saff, Edward B., and Arthur David Snider. (2002) Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics. 3rd ed. Upper Saddle River, NJ: Prentice Hall. ISBN: 0139078746.
http://math.sfsu.edu/beck/papers/complex.pdf
2. J.E. Marsdeen and M.J. Hoffman.,(1999) Basic Complex Analysis, W H Freeman, ISBN0-7167-2877-X
3. M.J. Ablowitz and A.S. Fokas.,(2003) Complex Variables, Introduction and Applications, Cambridge Texts in Applied Mathematics , ISBN 052153429
4. Brown and Churchill, (2009)Complex Variables and Applications,8th Ed., McGraw-Hill ,ISBN 978–0–07–305194–9
5. http://www.math.ucsb.edu/~wei/teach/122/Brown-Churchill-Complex%20Variab...)
Course ID: MATH 501
Credit hours | Theory | Practical | Laboratory | Lecture | Studio | Contact hours | Pre-requisite | 4 | 4 | 4 | MATH 301 |
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