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Quick Facts

Medium Of Instructions	Mode Of Learning	Mode Of Delivery
English	Self Study	Video and Text Based

Course Overview

The ‘Complex Analysis’ online certification course enables students to learn about the foundational level mathematics focussing on complex numbers and the complex analysis functions. This online course attempts to discuss the implications of complex numbers that offer the spectral theorem for matrices. This free National Program for Technology Enhanced Learning (NPTEL) course is provided by the Swayam education portal. It is a core course for undergraduate and postgraduate level students and is scheduled for twelve weeks. The classes are held online through videos, lectures, weekly assignments, and other online resources.

The instructor for this online training is Dr. Pranav Haridas, assistant professor at the Kerala school of mathematics. The students of this course are given an opportunity to explore the theoretical and practical implications of complex numbers in the mathematics domain.

The ‘Complex Analysis’ certification course ensures a course certificate and credit points after successfully completing this AICTE recognized course and the certification exam.

The Highlights

Online mode
Twelve weeks program
Free training
Core course
Credit points
E-Certificate

Programme Offerings

videos
Lectures
Online Classes
Weekly Assignments
Final Exam
course certificate
Credit Points

Courses and Certificate Fees

Fees Informations	Certificate Availability	Certificate Providing Authority
INR 1000	yes	Kerala School of Mathematics, Kozhikode

The ‘Complex Analysis’ certification fee should be paid online to register for the certification exam.

Complex Analysis fee structure

Program Fee	Nil
Exam Registration Fee	Rs. 1,000

Eligibility Criteria

The students applying for the ‘Complex Analysis’ online course should have prior knowledge of the mathematical concepts of real analysis and linear algebra.

Certificate qualifying details

The students of this training program will become eligible for the ‘Complex Analysis’ certification by Swayam after completing the course and assessments with a minimum score as the following,

Internal assessment – 10/25(25%) in the best 8 out of 12 assignments.
Final exam - 30/75(75%)
Overall average – 40/100

What you will learn

Mathematical skillKnowledge of engineering

The ‘Complex Analysis’ certification syllabus is framed for the students to gain a comprehensive understanding of the concepts and functions associated with complex numbers. This course enables students to familiarize themselves with the holomorphic functions and their fundamental properties such as Cauchy’s theorem and residue theorems, the categorization of singularities, and the maximum principle. By the end of the course, students will develop expertise in the singularities of holomorphic functions.

Who it is for

The ‘Complex Analysis’ online certification course is directed at the students pursuing the final year in their bachelor’s degree or first year of master’s degree in the field of mathematics or engineering. This course is also beneficial for individuals and professionals who work in engineering-based companies.

Admission Details

The students interested in joining the ‘Complex Analysis’ certification classes should register online through the course website.

Step 1: Find the course page using the link,

https://onlinecourses.nptel.ac.in/noc21_ma39/preview

Step 2: Click on the ‘Sign-In/Register’ option.

Step 3: Fill in the registration form.

Step 4: Start the course.

Application Details

The candidates of the ‘Complex Analysis’ certification course should enter the Swayam account details on the registration form if they already have an account or can create a new course account. The students can join the course using Google, Facebook, or Microsoft account IDs.

The Syllabus

Algebra and Topology of the complex plane

The geometry of the complex plane
Complex differentiation

Power series and its convergence
Cauchy-Riemann equations

Harmonic functions
Möbius transformations

Integration along a contour
The fundamental theorem of calculus

Homotopy
Cauchy’s theorem

Cauchy integral formula
Cauchy’s inequalities, and other consequences

Winding number
Open mapping theorem
Schwarz reflection Principle

Singularities of a holomorphic function
Laurent series

The residue theorem
Argument principle
Rouche’s theorem

Branch of the Complex logarithm
Automorphisms of the Unit disk

Covering spaces
Picard's theorem

Evaluation process

The end-term proctored exam is conducted for the students to become eligible for the ‘Complex Analysis’ certification by Swayam. The registration and payment for this exam are done online through the course website and the exam is conducted at the allotted exam centers. Students will have to score a minimum of 30/75(75%) in the exam to qualify for the certification.