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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 Fourier Analysis and Its Applications online course has been selected as the basic theoretical applications and aspects of the topics that are directly or indirectly related to the topic of Fourier.
The Fourier Analysis and Its Applications certification syllabus will be conducted for a total of 12 weeks and will be covering the topics namely- The space S of rapidly decreasing functions, Application to PDEs, Fourier transform as an operator from S to S, and the Plancherel's theorem, Cesaro summability - Fejer's theorem and its applications, Basic convergence theorem of Fourier series and its applications and Sturm-Liouville problems and its applications.
With the help of lecture videos, assignments, tests, and case study guides, the students will be taught the basics of the concept of Fourier. The diverse applications of the subject of mathematics will also be covered in a descriptive way in the online course on Fourier Analysis and Its Applications by Swayam.
The Highlights
- The course duration of 12 weeks
- The program provided by Swayam
- The program partnered by the Indian Institute of Technology, Bombay
- AICTE approved FDP course
- Course type - elective
Programme Offerings
- Self-assessments
- Reading Material
- case study
- online learning
- videos
- Quiz
- Lectures
- test.
Courses and Certificate Fees
| Fees Informations | Certificate Availability |
|---|---|
| INR 1000 | yes |
The fees for the course Fourier Analysis and its applications is -
| Fees type | Amount |
| Certificate exam | Rs. 1,000 |
Eligibility Criteria
Certification Qualification Details
The students will be getting the Fourier Analysis and Its Applications certification once they complete their course. Also, they need to appear for a final proctored exam. The candidates need to clear the exam.
What you will learn
In the Fourier Analysis and Its Applications training, students will learn about-
- Students will be learning about all the applications that are related to PDEs.
- Candidates will further study the application of Fejer’s theorem.
- The importance of mean convergence will also be discussed in the Fourier Analysis and Its Applications certification syllabus.
- Applicants will be provided classes of Fourier and its applications.
- Enrolled students will study the details of Plancherel's theorem.
- The Fourier transform as an operator from S to S will also be covered in the course curriculum.
- The applications of Sturm-Liouville problems will also be discussed.
Who it is for
The Fourier Analysis and Its Applications training is recommended to-
- Students who want to study and gather a detailed understanding of Fourier applications.
Application Details
For applying to the Fourier Analysis and Its Applications online course, the students need to follow the following steps-
Step 1: The students are requested to visit the link to generate the form- https://onlinecourses.nptel.ac.in/noc25_ma23/preview
Step 2: Candidates have to sign in or log in to the official site of Swayam.
Step 3: Candidates need to fill in all the necessary credentials and then register for the desired program.
The Syllabus
- Genesis
- Basic convergence theorem
- Mean convergence of Fourier series
- Cesaro summability and Fejer’s theorem
- Fourier transform (Introduction)
- Forier transform (Airy’s function, wave phenomenon and Ramanujan’s formula)
- Fourier Bessel expansions
- Generalized Fourier series
- Regular Sturm-Liouville problems
- Applications of functional analysis
- Hilbert Schmidt operators, Green’s functions and spectrum
- Spectral theorem for compact self-adjoint operators
- Celestial Mechanics
- Odds and Ends
- Return to classical Fourier series
- Tempered distributions
- Fourier transforms