Open mapping theorem,maximum modulus theorem complex numbers
Course Material
- Introduction to complex numbers
- Geometric representation of complex numbers,triangular inequality,complex conjugate
- Power and roots of complex ,argument of product and quotient
- Functions of complex variable,definition ,limit and continuity
- Branches of functions,differentiable and analytic functions,the Cauchy Riemann equations
- Entire functions, harmonic functions, the exponential function
- Elementary functions:trigonometric, hyperbolic functions
- Logarithmic and inverse elementary functions
- Mid Term Exam
- Open mapping theorem,maximum modulus theorem complex numbers
- Integrals:contours and contour integrals,Cauchy Goursat theorem,Cauchy integral formula
- Lioville's theorem,Morerea theorem,power series
- Series:radius of convergence and analyticity, Taylor's and Laurent's series
- Integration and differentiation of power series singularities
- Poles and residues:zeros,singularities, poles and residues
- Types of singular point ,calculus of residues contour integration
- Cauchy residue theorem with applications, Möbius transform,conformal mappings and transformation
- Final Term Exams
- Chapters 18
- Department Mathematics(SCB)
- Teacher
Nadia Aslam
