Sub. Code / Sub. Name: MA6351 Transform and Partial Differential Equations Unit IV : Fourier Transforms Statement of Fourier integral theorem Fourier transform pair Fourier sine Unit Syllabus: – – and cosine transforms Properties Transforms of simple functions Convolution theorem – – – identity. – Parseval’s Objective: To acquaint the student with Fourier transform techniques used in wide variety of situations. Session Teaching Topics to be covered Ref No * Aids Introduction to infinite Fourier transform and 1 Ch.4; – 25 LCD/BB Fourier integral theorem Pg.4.1 4.2 – 1 Ch.4; – 26 Fourier transforms pair and problems. LCD/BB Pg.4.4 4.5 & – Pg.4.11 4.15 – 1 Ch.4; – 27 More problems on Fourier transform pair LCD/BB Pg.4.23 4.26 – 28 Tutorial class Worksheet LCD/BB 1 Ch.4; – 29 Fourier cosine and sine transform and problems LCD/BB Pg.4.5 4.6 & – Pg.4.15 4.23 – More problems on Fourier sine and cosine 1 Ch.4; – 30 LCD/BB transform. Pg.4.23 4.26 – Properties of Fourier transforms, Fourier sine 1 Ch.4; – 31 LCD/BB transforms and cosine transforms. Pg.4.26 4.28 – 32 Tutorial class Worksheet LCD/BB 1 Ch.4; – 33 Transforms of simple functions and problems. LCD/BB Pg.4.29 4.31 & – Pg.4.37 4.41 – Derivation of Convolution theorem and Parseval’s 1 Ch.4; – 34 LCD/BB identity for Fourier transforms Pg.4.31 4.33 – Problems using identity and convolution Parseval’s 1 Ch.4; – 35 LCD/BB theorem Pg.4.37 4.41 – 36 Tutorial class Worksheet LCD/BB Content beyond syllabus covered (if any): Nil * Session duration: 50 mins
Sub. Code / Sub. Name: MA6351 Transform and Partial Differential Equations Unit IV : Fourier Transforms Unit Syllabus: Statement of Fourier integral theorem – Fourier transform pair – Fourier sine and cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity. Objective: To acquaint the student with Fourier transform techniques used in wide variety of situations. Session No * Topics to be covered Ref Teaching Aids 25 Introduction to infinite Fourier transform and Fourier integral theorem 1 – Ch.4; Pg.4.1 – 4.2 LCD/BB 26 Fourier transforms pair and problems. 1 – Ch.4; Pg.4.4 – 4.5 & Pg.4.11 – 4.15 LCD/BB 27 More problems on Fourier transform pair 1 – Ch.4; Pg.4.23 – 4.26 LCD/BB 28 Tutorial class Worksheet LCD/BB 29 Fourier cosine and sine transform and problems 1 – Ch.4; Pg.4.5 – 4.6 & Pg.4.15 – 4.23 LCD/BB 30 More problems on Fourier sine and cosine transform. 1 – Ch.4; Pg.4.23 – 4.26 LCD/BB 31 Properties of Fourier transforms, Fourier sine transforms and cosine transforms. 1 – Ch.4; Pg.4.26 – 4.28 LCD/BB 32 Tutorial class Worksheet LCD/BB 33 Transforms of simple functions and problems. 1 – Ch.4; Pg.4.29 – 4.31 & Pg.4.37 – 4.41 LCD/BB 34 Derivation of Convolution theorem and Parseval’s identity for Fourier transforms 1 – Ch.4; Pg.4.31 – 4.33 LCD/BB 35 Problems using Parseval’s identity and convolution theorem 1 – Ch.4; Pg.4.37 – 4.41 LCD/BB 36 Tutorial class Worksheet LCD/BB Content beyond syllabus covered (if any): Nil * Session duration: 50 mins