TEW - Complex Analysis, Transforms and Numerical Techniques (2022)

Speakers and Syllabus

 SPEAKERS, THEIR AFFILIATIONS, AND TOPICS

Speaker Affiliation Number of lecture hours Number of tutorial hours Detailed Topic(s)
G. P. Youvaraj RIASM, Chennai 9 2 (conduct) + 2 (assist)

Complex Analysis:
Holomorphic functions, Cauchy-Riemann equations, analytic functions
expressible as power series (Taylor series) and local properties of holomorphic
functions.
Singularities, Laurent series expansion, discussion of zeros and singularities of
analytic functions, Complex integration, Rouché’s theorem and applications of the
Residue Theorem, with an emphasis on computing/estimating improper Riemann
integrals via contour integration.
Linear transformations, linear fractional transformations, mappings of the upper
half plane and mappings by the Exponential function.
Ramesh Kasilingam IIT Madras 9 2 (conduct) + 2 (assist) Transforms:
Fourier series representation of continuous and discrete time periodic
signals, applications of Fourier transform for continuous and discrete time
signals, Fourier transform pair, Convolution theorem and Parseval’s
identity.
Laplace transform and its properties, Transform of periodic functions,
Inverse Transforms and application to solution of linear ODE with constant
coefficients.
Z-transform, Elementary properties, Inverse Z-transform and Solution of
difference equation using Z-transform.
Y. V. S. S. Sanyasiraju IIT Madras 9 2 (conduct) + 2 (assist)  Numerical Techniques:
Introduction to error analysis, solutions of linear system of equations by fixed-
point and Gauss-Seidel iterative methods and their convergence.
Interpolation: Lagrange, Spline Interpolation and Least square method for
curve fitting. Eigenvalues of a matrix by Power method and numerical
differentiation and integration (Basic idea).
Numerical solutions for first order ODEs. We will use MATLAB to solve
practical problems.

References:

  1. James Ward Brown and Ruel V. Churchill, “Complex Variables and Applications”, McGraw-Hill Education, 9th Edition, 2014.
  2.  Erwin Kreyszig, “Advanced Engineering Mathematics”, John Wiley & Sons Pvt. Ltd, Singapore, 9th Edition, 2006, (Reprint 2013).

 

Time Table

 

Time 09:30 to 11:00   11:15 to 12:45   14:00 to 15:30   15:45 to 16:45   
  Lecture   Lecture   Lecture   Tutorial  
Mon 4th GPY   RK L YVSSS   GPY & RK S
Tue 5th YVSSS T GPY U RK T YVSSS & GPY N
Wed 6th RK E YVSSS N GPY E RK & YVSSS A
Thu 7th GPY A RK C YVSSS A GPY & RK C
Fri 8th YVSSS   GPY H RK   YVSSS & GPY K
Sat 9th RK   YVSSS   GPY   RK & YVSSS S

 

  • GPY = G. P. Youvaraj,
  • YVSSS = Y. V. S. S. Sanyasiraju
  • RK = Ramesh Kasilingam

GPY – 9 lecture hours + 4 tutorial hours;
YVSSS – 9 lecture hours + 4 tutorial hours;
RK – 9 lecture hours + 4 tutorial hours

Note: Tutorials will be conducted by one speaker and will be assisted by another speaker.
Note: Last date for receiving online application forms: 15 th June (Wednesday), 2022.
Note: Selected list of applicants will be available on 25th June (Saturday), 2022.

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