| Course Name | Complex Analysis |
| Course Code | 25MAT311 |
| Program | B. Sc. in Physics, Mathematics & Computer Science (with Minor in Artificial Intelligence and Data Science) |
| Semester | 6 |
| Credits | 3 |
| Campus | Mysuru |
Definition – Algebra of complex numbers – polar forms – regions – Limits – continuity – differentiability – CR equations – Analytic Functions – Harmonic Functions.(Chapters 1 & 2)
Conformal mappings – bilinear transformations – Special bilinear transformations – fixed points.
Chapter-9 (Sections: 9.1-9.4)
Introduction to complex Integration – Contour integral – Primitives – Cauchy-Goursat theorem – Winding number – Cauchy’s integral formula.
Chapter-4 (Sections: 4.1-4.4, 4.6, 4.7)
Sequences – series – power series – uniform convergence of power series – Taylor’s series – Laurent’s series – Integration and differentiation of Power series.
Chapters- 5 & 6 (Sections: 5.1-5.2, 6.1-6.3,6.5,6.6)
Zeros and singularities of analytic functions – types of singularities – poles – residue theorem.
Chapter-7 (Sections: 7.1-7.3)
Classification of Singularities – Residues – Poles and zeroes.
Chapter-7 (Sections: 7.1-7.3)
Course Objectives
1) To obtain knowledge of theory of complex functions of a complex variable.
2) To get acquainted with different methods and techniques of series.
3) To get acquainted with different methods and techniques of bilinear transformations.
Course Outcomes:
| COs | Description |
| CO1 | Explain the concepts of Analytic function, Cauchy- Riemann equations and Harmonic function. |
| CO2 | Apply the concept of mapping like translation, rotation, magnification and inverse. |
| CO3 | Apply and analyze to solve problem using contour integral. |
| CO4 | Application of Taylor’s series, Lourent’s series to solve problems. |
| CO5 | Evaluate using the concept of Singularities, poles, residue theorem. |
| PO/PSO |
PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PO6 |
PO7 |
PO8 |
PO9 |
PO10 |
PSO1 |
PSO2 |
PSO3 |
PSO4 |
| CO | ||||||||||||||
| CO1 | 2 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 1 | 2 | – |
| CO2 | 3 | – | 1 | 3 | 2 | – | 2 | – | – | – | – | 1 | 3 | – |
| CO3 | 2 | – | 2 | 3 | 2 | – | 2 | – | – | – | – | 1 | 2 | – |
| CO4 | 2 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 1 | 3 | – |
| CO5 | 2 | – | 3 | 3 | 2 | – | 2 | – | – | – | – | 1 | 2 | – |
TEXTBOOKS:
1) H S Kasana, Complex variables and Theory and Applications, 2nd edition, Prentice Hall India.
REFERENCES:
1) S. Ponnusamy, Foundations of Complex Analysis, 2nd Edition, Narosa Publishing House, 2005.
2) J.W. Brown and R.V. Churchil, Complex Variable and Applications, 8th edition, McGraw Hill, 2008.
3)R. Roopkumar, Complex Analysis, 1st edition, Pearson Education, Chennai, 2014.
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