.png)
Department of Mathematics, J.C. Bose University of Science and Technology, YMCA, Faridabad, Haryana has organised the two days workshop on “Recent Trends in Complex Analysis” sponsored by Haryana State Council of Science, Innovation and Technology (HSCSIT) . The workshop is being organized from 9th February-10th February 2022. More than 150 participants from different universities have registered for the workshop. The workshop is specially intended for UG/PG students and faculty members of Mathematics. The content of the course is designed in such a way that even beginners are benefited by attending the workshop.
Topics related to complex analysis like analytic functions, Cauchy’s Riemann equations , Taylor’s and Laurent series, singularities and zeros of analytic functions, residues and conformal mapping have important roles in all the aspects of Science and Engineering. This workshop will be beneficial for undergraduate and post graduate students to explore the field of complex analysis It is helpful in many branches of mathematics, including algebraic geometry, number theory, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and particularly quantum mechanics.
On this occasion, Dr. Neetu Gupta, Chairperson of the Department, has welcomed worthy Registrar sir Prof. Sunil Kumar Garg, the chief guest, Prof. Vijay Gupta who is Professor in Department of Mathematics, Netaji Subhas University of Technology, Delhi, Prof.Ashutosh Dixit Dean, Faculty of Sciences and Faculty of Life Sciences, J.C. Bose University of Science and Technology, YMCA, Dr. Anuradha Gupta, Associate Professor, Department of Mathematics, Delhi College of Arts and Commerce, University of Delhi and all the participants of the course. Then she briefed about the two days workshop. She mentioned that many problems which may be difficult to solve in the real domain can be more easily solved when transformed into complex variables due to a number of special properties of the complex domain. She also told that the department has successfully organized many workshops, seminars, value added courses, expert lectures and various competitions for students during the past one year.
Prof. Ashutosh Dixit explained about the field of complex Analysis. He told that despite the name being ‘imaginary’, the impact of the field is most certainly real. Indeed, complex numbers have applications in the real world, particularly in engineering. He suggested to take some assignments from the students for getting more benefit of the workshop.
Then, Hon’ble Registrar sir, Prof. Sunil Kumar Garg explained the significance of learning Mathematics by the future engineers of the university. He described the expertise of the chief guest, Prof. Vijay Gupta. He also mentioned that Mathematics is an important domain in science and technology. It is the universal language that is applied in almost every aspect of life.
In the keynote address, the chief guest, Prof. Vijay Gupta gave a brief introduction about the uses of Complex Analysis in different fields of mathematics. He told that Jiffy is an actual unit of time for 1/100th of a second and zero is not there in roman numerals.
The inaugural event ended with a vote of thanks by Chairperson of the Department of Mathematics, Prof. Neetu Gupta. She congratulated the co-ordinator Dr. Manu Rohilla, co-coordinator Dr. Parveen Kumar and faculty members for organizing the workshop.
Session-1 (February 9, 2022)
Speaker of session: Dr. Anuradha Gupta
Time: 10:45 A.M. to 12:00 Noon
Topic: Historical Introduction and Overview of Complex Analysis, Analytic Functions, Cauchy-Riemann Equations
The topic of the session was Historical Introduction and Overview of Complex Analysis, Analytic Functions, Cauchy-Riemann Equations. Dr. Anuradha Gupta gave a brief history of the origin of complex analysis citing various works done between 12th century and 16th century. She discussed the work of Rene Descartes in his book La Geometrie in which the concept of Cartesian geometry was introduced. She told that Leonhard Euler introduced the concept of i=?(-1). Euler started writing a complex number as
x+iy=r(cos??+i sin?? ).
She explained that W.R. Hamilton gave the algebraic definition of complex numbers. However, in 19th century, Carl Friedrich introduced the term complex numbers. She discussed the triangle inequality, topological aspects of the complex plane, complex valued functions, differentiability and analyticity of complex valued functions, entire functions, Cauchy-Riemann equations. In the last, Dr. Anuradha Gupta discussed the relation between analytic and harmonic functions.
Session-2 (February 9, 2022)
Speaker of session: Prof. R.C. Mittal
Time: 12:00 P.M. to 01:15 P.M.
Topic: Taylor and Laurent series expansion, Singularities
Prof. R.C. Mittal discussed how to find Laurent series of a function. Then, he explained singularities and its types with some examples.
Session-3 (February 9, 2022)
Speaker of session: Dr. Sushil Kumar
Time: 02:00 P.M. to 03:15 P.M.
Topic: Zeroes of Analytic Functions, Complex Integration, Cauchy’s Theorem
Dr. Sushil Kumar described about zeroes of analytic Functions, complex integration and Cauchy’s theorem. He also discussed about different important topics of complex analysis like simply and multi connected regions, Cauchy Goursat theorem etc.
Session-4 (February 10, 2022)
Speaker of session: Dr. Anuradha Gupta
Time: 10:00 A.M. to 11:15 A.M.
Topic: Calculus of residues
Dr. Anuradha Gupta explained various topics like contour, punctured disk, residue, singularities and its different types, Cauchy’s Residue Theorem, Complex integration with examples. She also introduced the different method to find the residue for simple pole, for poles of order k and for essential singularity. She solved many problems related to above mentioned topics. She also cleared all the doubts/queries of the participants successfully. Participants were quite satisfied after her talk.
Session-5 (February 10, 2022)
Speaker of session: Prof. R.C. Mittal
Time: 11:15 P.M. to 12:30 P.M.
Topic: Conformal Mapping
In the session, Prof. R.C. Mittal explained in detail about Conformal Mapping. He started his presentation by telling us the importance of Conformal Mapping. He briefly described bilinear transformations and illustrated using relevant examples.
Session-6 (February 10, 2022)
Speaker of session: Prof. S.S. Chauhan
Time: 02:00 P.M. to 03:15 P.M.
Topic: Argument Principle, Rouche’s Theorem
Prof. S.S. Chauhan discussed about how complex number came into existence. Then he explained some real life applications and mathematical applications. He has discussed Argument principle and Rouche’s Theorem.
The program ended with vote of thanks by Prof. Neetu Gupta, Chairperson Department of Mathematics. She congratulated the co-ordinator Dr. Manu Rohilla, co-coordinator Dr. Parveen Kumar, faculty members and the student organizing team-Shrishti, Dipakshi and Dipakshi for organizing the workshop.