IST - Geometry of Complex Functions (2021)
Speakers and Syllabus
Name of the speakers with affiliation and syllabus
|
Name of the Speaker |
Number of Lectures (1.5 hrs per lecture) |
Syllabus |
|
Dr. Sourav Pal IIT Bombay |
4 Lectures (6 hours) |
Definition and Geometric Interpretation of Complex Numbers, Topology of the Complex Plane, Definition and Geometric Representation of Complex Functions, Power Functions and , Elementary Functions: Exponential Function, Logarithmic Functions, Branch cut and branch points, Complex Exponents, Trigonometric and Hyperbolic Functions, Inverse Trigonometric and Hyperbolic Functions |
|
Dr. Ved Datar IISc Bangalore |
4 Lectures (6 hours) |
Limits and Continuity of and comparison with , Reciprocal Transformations , Riemann Sphere, Stereographic Projection, Differentiability, Cauchy-Riemann Equations, Analytic Functions, Entire Functions, Harmonic Functions, Analyticity of Complex and Real Functions |
|
Dr. Vamsi Pritham Pingali IISc Bangalore |
4 Lectures (6 hours) |
Definition, Properties and Geometric Interpretation of Conformal Mapping, Mobius Transformation, Fixed Point, Automorphisms of the Disc, Reflection Principle, Open Mapping Theorem, Schwarz Lemma |
|
Dr. Sushil Gorai IISER Kolkata |
4 Lectures (6 hours) |
Curves in the Complex Plane, Contours, Line Integrals, Cauchy’s Theorem, Contour Integrals, Winding Number, Homotopy version of Cauchy’s Theorem, Multiply Connected Domains, Cauchy Integral Formula |
|
Dr. Swadesh Kumar Sahoo IIT Indore |
4 Lectures (6 hours) |
Cauchy’s Inequality and Applications, Liouville’s Theorem, Maximum Modulus Principle, Power Series, Radius of Convergence, Taylor and Laurent Series, Singularities and its Classification |
|
Dr. Vasudeva Rao Allu IIT Bhubaneswar |
4 Lectures (6 hours) |
Zeros, Poles, Meromorphic Functions, Cauchy Residue Theorem, Evaluation of Real Trigonometric Integrals and Improper Integrals, Integration along a Branch cut |
Reference Books:
- S. Ponnusamy, Foundations of Complex Analysis, Narosa Pusblishing House, Second Edition.
- E.M. Stein, R. Shakarchi, Complex Analysis, Princeton University Press
- Theodore W. Gamelin, Complex Analysis, Springer.
- Dennis G. Zill, P.D. Shanahan, A First Course in Complex Analysis with Applications, Jones and Bartlett Publishers, Canada
- John B. Conway, Functions of One Complex Variable, Springer.
- W. Rudin, Real and Complex Analysis, McGraw Hill Publication
Name of Tutors
- Dr. Md Firoz Ali, Assistant Professor, Department of Mathematics,National Institute of Technology Durgapur, West Bengal.
- Dr. Manas Ranjan Mohapatra, Visiting Faculty, Institute of Mathematics and Applications, Bhubaneswar, Odisha.
- Dr. Ram Baran Verma, Assistant Professor, Department of Mathematics, SRM University, Andhra Pradesh.
- Dr. Molla Basir Ahamed, Postdoctoral Fellow, IIT Bhubaneswar, Odisha.
Time Table
Week 1
-
Date
14.07.2021
15.07.2021
16.07.2021
16.07.2021
17.07.2021
17.07.2021
18.07.2021
18.07.2021
Day
Wednesday
Thursday
Friday
Friday
Saturday
Saturday
Sunday
Sunday
Time
05:00 PM
–
06:30 PM
05:00 PM
–
06:30 PM
05:00 PM
–
06:30 PM
06:45 PM
–
07:45 PM
05:00 PM
–
06:30PM
06:45 PM
–
07:45 PM
04:00 PM –
05:30 PM
06:00 PM
–
07:30 PM
Lectures/
Tutorials
L – 1
SP
L – 2
SP
L – 3
SP
T – 1
RBV
L – 4
SP
T – 2
RBV
L – 5
VD
L – 6
VD
Week 2
|
Date |
21.07.2021 |
22.07.2021 |
23.07.2021 |
23.07.2021 |
24.07.2021 |
24.07.2021 |
25.07.2021 |
25.07.2021 |
|
Day |
Wednesday |
Thursday |
Friday |
Friday |
Saturday |
Saturday |
Sunday |
Sunday |
|
Time |
05:00 PM – 06:30 PM |
05:00 PM – 06:30 PM |
05:00 PM – 06:30 PM |
06:45 PM – 07:45 PM |
05:00 PM – 06:30PM |
06:45 PM – 07:45 PM |
04:00 PM – 05:30 PM |
06:00 PM – 07:30 PM |
|
Lectures/ Tutorials |
L – 1 VD |
L – 2 VD |
L – 3 VPP |
T – 1 MBA |
L – 4 VPP |
T – 2 MBA |
L – 5 VPP |
L – 6 VPP |
Week 3
|
Date |
28.07.2021 |
29.07.2021 |
30.07.2021 |
30.07.2021 |
31.07.2021 |
31.07.2021 |
01.08.2021 |
01.08.2021 |
|
Day |
Wednesday |
Thursday |
Friday |
Friday |
Saturday |
Saturday |
Sunday |
Sunday |
|
Time |
05:00 PM – 06:30 PM |
05:00 PM – 06:30 PM |
05:00 PM – 06:30 PM |
06:45 PM – 07:45 PM |
05:00 PM – 06:30PM |
06:45 PM – 07:45 PM |
04:00 PM – 05:30 PM |
06:00 PM – 07:30 PM |
|
Lectures/ Tutorials |
L – 1 SG |
L – 2 SG |
L – 3 SG |
T – 1 MRM |
L – 4 SG |
T – 2 MRM |
L – 5 SKS |
L – 6 SKS |
Week4
|
Date |
04.08.2021 |
05.08.2021 |
06.08.2021 |
06.08.2021 |
07.08.2021 |
07.08.2021 |
08.08.2021 |
08.08.2021 |
|
Day |
Wednesday |
Thursday |
Friday |
Friday |
Saturday |
Saturday |
Sunday |
Sunday |
|
Time |
05:00 PM – 06:30 PM |
05:00 PM – 06:30 PM |
05:00 PM – 06:30 PM |
06:45 PM – 07:45 PM |
05:00 PM – 06:30PM |
06:45 PM – 07:45 PM |
04:00 PM – 05:30 PM |
06:00 PM – 07:30 PM |
|
Lectures/ Tutorials |
L – 1 SKS |
L – 2 SKS |
L – 3 VRA |
T – 1 MFA |
L – 4 VRA |
T – 2 MFA |
L – 5 VRA |
L – 6 VRA |
|
L – Lecture T – Tutorial |
SP – Sourav Pal VD – Ved Datar VPP – Vamsi Pritham Pingali |
SG – Sushil Gorai SKS – Swadesh Kumar Sahoo VRA – Vasudeva Rao Allu |
RBV – Ram Baran Verma MRM – Manas Ranjan Mohapatra |
MFA – Md Firoz Ali MBA – Molla Basir Ahamed |