Complex Analysis
Develop your knowledge of the fundamental concepts and theorems of complex numbers and functions in this course.
Online
12 Weeks
Free 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
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.
Instructors
Kerala School of Mathematics, Kozhikode Frequently Asked Questions (FAQ's)
The students are required to have knowledge of linear algebra and real analysis.
The course is scheduled for twelve weeks.
The NPTEL course is provided by Swayam.
No, you will get an E-Certificate after completing the course.
You can get three credit points for this certification.