Understanding Fourier Series and Its Applications
delves into the concept of Fourier Series, exploring periodic functions, harmonic analysis, and real-world applications. Learn about its origins from Joseph Fourier and its significance in various fields.
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Fourier Series Prof. Mandar Vijay Datar Department of Engineering Sciences International Institute of Information Technology, I IT www.isquareit.edu.in
Fourier Series Fourier Series Learning Objectives:- LO1:- Periodic Functions and their expansion as Fourier Series LO2:- Half range and Full range Fourier Series and their formulation LO3:- Harmonic Analysis of Discrete functions LO4:- Applications of Fourier Series Joseph Fourier (1768-1830) International Institute of Information Technology, I IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www.isquareit.edu.in | Email - info@isquareit.edu.in
How it Starts It starts with the attempt of solving Heat Conduction equation. French mathematician Joseph Fourier (1768 1830) was trying to solve this problem He needed to express a function as an infinite series of sine and cosine functions Before Fourier, Bernoulli and Euler made similar attempts while solving problems of vibrating strings International Institute of Information Technology, I IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www.isquareit.edu.in | Email - info@isquareit.edu.in
Definition International Institute of Information Technology, I IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www.isquareit.edu.in | Email - info@isquareit.edu.in
Example Consider the following function International Institute of Information Technology, I IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www.isquareit.edu.in | Email - info@isquareit.edu.in
Example Continued.... We follow the steps as given in the definition of Fourier Series- International Institute of Information Technology, I IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www.isquareit.edu.in | Email - info@isquareit.edu.in
Example Continued.... Therefore the Fourier Series of given function is- International Institute of Information Technology, I IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www.isquareit.edu.in | Email - info@isquareit.edu.in
Fourier Series for Arbitrary Period International Institute of Information Technology, I IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www.isquareit.edu.in | Email - info@isquareit.edu.in
Excercise You can Try following Problems and Find their Fourier series expansion International Institute of Information Technology, I IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www.isquareit.edu.in | Email - info@isquareit.edu.in
For More Details Contact: - Prof. Mandar Vijay Datar mandard@isquareit.edu.in Mob. No. 9422615876 International Institute of Information Technology, I IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www.isquareit.edu.in | Email - info@isquareit.edu.in
