Week 15: Isolated Singular Point, Introduction to Residues, Introduction to Cauchy’s residue theorem with applications, Residue at Infinity
Churchill R. V., J. W. Brown. Complex Variables and Applications ,9th ed. (McGraw Hill, New York, 1989)
pgs 227 - 235, 238 - 242
Course Material
- Week1: Introduction to Complex Numbers, Basic Algebraic Properties
- Week 02: Introduction to Geometric representation of complex numbers
- Week 03:Introduction to Powers and roots of complex numbers
- Week 4: Introduction to Functions of Complex Variables: Definition, limit and continuity
- Week 05: Introduction to Differentiable and analytic functions
- Week 06: Introduction to Cauchy-Riemann equations, Entire functions, Harmonic functions
- Week 07: Introduction to Elementary functions: The exponential and the Logarithmic Function, Branches of Logarithmic function1
- Week 08: Introduction toTrigonometric, Hyperbolic and Inverse trigonometric and hyperbolic functions
- Week 09: Mid Term Exam
- Week 10: Introduction to Complex Integrals: Contours and contour integrals
- Week 11: Upper bounds for the moduli of Contour Integral, Introduction to Cauchy-Goursat theorem, Cauchy integral formula
- Week 12: Lioville’s theorem, Introduction to Open mapping theorem. Maximum modulus theorem
- Week 13: Power series, Radius of convergence and analyticity, Introduction to Taylor’s and Maclaurin series191
- Week 14: Laurent Series, Integration and differentiation of power series, Multiplication and division of power series
- Week 15: Isolated Singular Point, Introduction to Residues, Introduction to Cauchy’s residue theorem with applications, Residue at Infinity
- Week 16: The Three Types of Isolated Singular Points, Residue at Poles, Zero of Analytic Function,
- Week 17: Mobius transforms, Conformal mappings and transformations
- Week 18: Final Term Exam
- Chapters 18
- Department Mathematics
- Teacher
Ms. Asifa Ilyas
