Media Storage Type : DVD-ROM
NPTEL Course Name : Complex Analysis
NPTEL Subject Matter Expert : Dr. A. Swaminathan
NPTEL Co-ordinating Institute : IIT Roorkee
NPTEL Lecture Count : 42
Lecture Titles:
Lecture 1 - Number system
Lecture 2 - Algebra of Complex Numbers
Lecture 3 - Inequalities and complex exponents
Lecture 4 - Topology of the Complex Plane
Lecture 5 - Stereographic Projection
Lecture 6 - Limit, Continuity and Differentiability
Lecture 7 - Analytic functions
Lecture 8 - Cauchy?Riemann equations
Lecture 9 - Singular points and Applications to the problem of Potential Flow
Lecture 10 - Harmonic functions
Lecture 11 - Complex sequences, series and their Convergence
Lecture 12 - Uniform convergence and Power Series
Lecture 13 - Elementary functions
Lecture 14 - Hyperbolic functions and Logarithmic functions
Lecture 15 - Parametric Integration
Lecture 16 - Contour Integration and Cauchyï¾’s theorem
Lecture 17 - Cauchy Integral Formula
Lecture 18 - Consequences of Cauchy integral formula
Lecture 19 - Maximum modulus principle and Schwarz lemma
Lecture 20 - Taylor series
Lecture 21 - Laurent Series
Lecture 22 - Zeros and singularities
Lecture 23 - Residue at a singularity
Lecture 24 - Quotients of Analytic functions
Lecture 25 - Contour integration and applications
Lecture 26 - Evaluation of improper integrals
Lecture 27 - Examples on improper integrals
Lecture 28 - Conformal Mapping
Lecture 29 - Special transformations
Lecture 30 - Bilinear Transformation
Lecture 31 - The mapping w= exp(z)
Lecture 32 - The mapping w=1/z
Lecture 33 - The mapping w=z^2 and its inverse mapping
Lecture 34 - The mapping w=sin z
Lecture 35 - Application to steady temperature
Lecture 36 - Electro static potential
Lecture 37 - Two dimensional fluid flow and Stream function
Lecture 38 - Schwarz Christoffel Transformation
Lecture 39 - Schwarz Christoffel Transformation (Continued...)
Lecture 40 - Poisson integral formula for the disc and plane
Lecture 41 - Dirichlet problem for the disc and the plane
Lecture 42 - Neumann problem for the disc and the plane