Sub. Code / Sub. Name: MA6351 Transform and Partial Differential Equations Unit : Applications of Partial Differential Equations Unit Syllabus: Classification of PDE – Method of separation of variables - Solutions of one dimensional wave equation – One dimensional equation of heat conduction – Steady state solution of two dimensional equation of heat conduction (excluding insulated edges). Objective: To know how to apply Fourier series to get the solution of wave and heat equations. Session No * Topics to be covered Ref Teaching Aids 13 Introduction and Classification of . 5 – Ch.19; Pg. 19.1 – 19.3 LCD/BB 14 Method of separation of variables. 2 – Ch.18; Pg. 657 – 658 LCD/BB 15 Solutions of one dimensional wave equation by method of separation of variables 1 – Ch.3; Pg.3.6 – 3.8 LCD/BB 16 Problems on wave equation with the given initial and boundary conditions 1 – Ch.3; Pg.3.10 – 3.60 LCD/BB 17 Tutorial class Worksheet LCD/BB 18 Solution of one-dimensional heat equation by method of separation of variables 1 – Ch.3; Pg.3.63 – 3.65 LCD/BB 19 Problems on heat equation with the given initial and boundary conditions 1 – Ch.3; Pg.3.65 – 3.113 LCD/BB 20 Tutorial class Worksheet LCD/BB Continuous Assessment Test-I 21 Steady state solution of two dimensional equation of heat conduction by method of separation of variables 1 – Ch.3; Pg.3.117 – 3.119 LCD/BB 22 Problems on equation for a finite plate. 1 – Ch.3; Pg.3.119 – 3.163 LCD/BB 23 Problems on equation for a semi - infinite plate. 1 – Ch.3; Pg.3.119 – 3.163 LCD/BB 24 Tutorial class Worksheet LCD/BB Content beyond syllabus covered (if any): Knowledge of heat transfer in circular plate is included. * 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