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Mathematics
Complex Analysis (Web)
Syllabus
Co-ordinated by :
IIT Roorkee
Available from :
2014-05-02
Lec :
1
Modules / Lectures
Introduction
Number system
Algebra of Complex Numbers
Inequalities and complex exponents
Functions of a Complex Variable
Topology of the Complex Plane
Stereographic Projection
Limit, Continuity and Differentiability
Analytic functions
Cauchy?Riemann equations
Singular points and Applications to the problem of Potential Flow
Harmonic functions
Sequences and Series
Complex sequences, series and their Convergence
Uniform convergence and Power Series
Elementary functions
Hyperbolic functions and Logarithmic functions
Complex Integration
Parametric Integration
Contour Integration and Cauchy’s theorem
Cauchy Integral Formula
Consequences of Cauchy integral formula
Consequences of complex integration
Maximum modulus principle and Schwarz lemma
Taylor series
Laurent Series
Zeros and singularities
Residue calculus
Residue at a singularity
Quotients of Analytic functions
Contour integration and applications
Evaluation of improper integrals
Examples on improper integrals
Conformal Mapping
Conformal Mapping
Special transformations
Bilinear Transformation
Mapping of Elementary transformation
The mapping w= exp(z)
The mapping w=1/z
The mapping w=z^2 and its inverse mapping
The mapping w=sin z
Applications of conformal mapping
Application to steady temperature
Electro static potential
two dimensional fluid flow and Stream function
Further theory of analytic functions
Schwarz Christoffel Transformation
Schwarz Christoffel Transformation (continued)
Poisson integral formula for the disc and plane
Dirichlet problem for the disc and the plane
Neumann problem for the disc and the plane
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