Week 12: Lioville’s theorem, Introduction to Open mapping theorem. Maximum modulus theorem
Churchill R. V., J. W. Brown. Complex Variables and Applications ,9th ed. (McGraw Hill, New York, 1989)
page 172-177
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
