# MA8353 Transforms and Partial Differential Equations Regulation 2017 Anna University

## OBJECTIVES :

 To introduce the basic concepts of PDE for solving standard partial differential equations.
 To introduce Fourier series analysis which is central to many applications in engineering apart from its use in solving boundary value problems.
 To acquaint the student with Fourier series techniques in solving heat flow problems used in various situations.
 To acquaint the student with Fourier transform techniques used in wide variety of situations.
 To introduce the effective mathematical tools for the solutions of partial differential equations that model several physical processes and to develop Z transform techniques for discrete time systems.

### UNIT I PARTIAL DIFFERENTIAL EQUATIONS 12

Formation of partial differential equations – Singular integrals – Solutions of standard types of first order partial differential equations – Lagrange’s linear equation – Linear partial differential equations of second and higher order with constant coefficients of both homogeneous and non-homogeneous types. MA8353 transforms and partial differential equations

#### UNIT II FOURIER SERIES 12

Dirichlet’s conditions – General Fourier series – Odd and even functions – Half range sine series – Half range cosine series – Complex form of Fourier series – Parseval’s identity – Harmonic analysis.

##### UNIT III APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS 12

Classification of PDE – Method of separation of variables – Fourier Series Solutions of one dimensional wave equation – One dimensional equation of heat conduction – Steady state solution of two dimensional equation of heat conduction. MA8353 transforms and partial differential equations

###### UNIT IV FOURIER TRANSFORMS 12

Statement of Fourier integral theorem – Fourier transform pair – Fourier sine and cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity.

###### UNIT V Z – TRANSFORMS AND DIFFERENCE EQUATIONS 12

Z-transforms – Elementary properties – Inverse Z-transform (using partial fraction and residues) – Initial and final value theorems – Convolution theorem – Formation of difference equations – Solution of difference equations using Z – transform.

OUTCOMES :

Upon successful completion of the course, students should be able to:
 Understand how to solve the given standard partial differential equations.
 Solve differential equations using Fourier series analysis which plays a vital role in engineering applications.
 Appreciate the physical significance of Fourier series techniques in solving one and two dimensional heat flow problems and one dimensional wave equations.
 Understand the mathematical principles on transforms and partial differential equations would provide them the ability to formulate and solve some of the physical problems of engineering.
 Use the effective mathematical tools for the solutions of partial differential equations by using Z transform techniques for discrete time systems.

TEXT BOOKS:

1. Grewal B.S., “Higher Engineering Mathematics”, 43rd Edition, Khanna Publishers, New Delhi, 2014.
2. Narayanan S., Manicavachagom Pillay.T.K and Ramanaiah.G “Advanced Mathematics for Engineering Students”, Vol. II & III, S.Viswanathan Publishers Pvt. Ltd, Chennai, 1998.

REFERENCES :

1. Andrews, L.C and Shivamoggi, B, “Integral Transforms for Engineers” SPIE Press, 1999.
2. Bali. N.P and Manish Goyal, “A Textbook of Engineering Mathematics”, 9th Edition, Laxmi Publications Pvt. Ltd, 2014.
3. Erwin Kreyszig, “Advanced Engineering Mathematics “, 10th Edition, John Wiley, India, 2016.
4. James, G., “Advanced Modern Engineering Mathematics”, 3rd Edition, Pearson Education, 2007.

### Course Curriculum

 UNIT 1 MA8353 UNIT1 INTRODUCTION FREE 00:00:00 MA8353 UNIT1 CHAPTER1 INTRODUCTION FORMATION OF PARTIAL DIFFERENTIAL EQUATION BY ELIMINATION OF ARBITRARY CONSTANT FREE 00:00:00 MA8353 UNIT1 CHAPTER1 TYPE1 PROBLEM1 FREE 00:00:00 MA8353 UNIT1 CHAPTER1 TYPE1 PROBLEM2,3 FREE 00:00:00 MA8353 UNIT1 CHAPTER1 TYPE1 PROBLEM4,5 FREE 00:00:00 MA8353 UNIT1 CHAPTER1 TYPE2 FORMATION OF PARTIAL DIFFERENTIAL EQUATION BY ELIMINATION OF ARBITRARY FUNCTIONS – PROBLEM1 FREE 00:00:00 MA8353 UNIT1 CHAPTER1 TYPE2 PROBLEM2 FREE 00:00:00 MA8353 UNIT1 CHAPTER1 TYPE2 PROBLEM3 FREE 00:00:00 MA8353 UNIT1 CHAPTER1 TYPE2 PROBLEM4,5 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPES OF FIRST ORDER NON LINEAR PARTIAL DIFFERENTIAL EQUATION – TYPE1 – PROBLEM1 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE1 PROBLEM2,3 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE2 PROBLEM1 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE2 PROBLEM2 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE2 PROBLEM3,4 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE2 PROBLEM5,6 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE3 PROBLEM1 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE3 PROBLEM2,3 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE3 PROBLEM4,5 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE4 PROBLEM1,2 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE4 PROBLEM3,4 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE4 PROBLEM5,6 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE5 INTRODUCTION FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE5 PROBLEM1 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE5 PROBLEM2,3 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE6 PROBLEM1 FREE 00:00:00 MA8353 UNIT1 CHAPTER2 TYPE6 PROBLEM2 FREE 00:00:00 MA8353 UNIT1 CHAPTER3 LAGRANGE’S LINEAR EQUATION METHOD OF GROUPING – PROBLEM1 FREE 00:00:00 MA8353 UNIT1 CHAPTER3 METHOD OF GROUPING – PROBLEM2,3 FREE 00:00:00 MA8353 UNIT1 CHAPTER3 METHOD OF GROUPING – PROBLEM1 & METHOD OF MULTIPLIER PROBLEM1 FREE 00:00:00 MA8353 UNIT1 CHAPTER3 METHOD OF MULTIPLIER – PROBLEM2,3 FREE 00:00:00 MA8353 UNIT1 CHAPTER3 METHOD OF MULTIPLIER – PROBLEM4 FREE 00:00:00 MA8353 UNIT1 CHAPTER3 METHOD OF MULTIPLIER PROBLEM5 FREE 00:00:00 MA8353 UNIT1 CHAPTER3 METHOD OF MULTIPLIER PROBLEM6 FREE 00:00:00 MA8353 UNIT1 CHAPTER3 METHOD OF MULTIPLIER PROBLEM7 FREE 00:00:00 MA8353 UNIT1 CHAPTER3 METHOD OF MULTIPLIER PROBLEM8 FREE 00:00:00 MA8353 UNIT1 CHAPTER4 HOMOGENEOUS EQUATION – PROBLEM1,2 FREE 00:00:00 MA8353 UNIT1 CHAPTER4 TYPE1 PROBLEM1,2 FREE 00:00:00 MA8353 UNIT1 CHAPTER4 TYPE1 PROBLEM3,4 FREE 00:00:00 MA8353 UNIT1 CHAPTER4 TYPE2 PROBLEM1 FREE 00:00:00 MA8353 UNIT1 CHAPTER4 TYPE2 PROBLEM2 FREE 00:00:00 MA8353 UNIT1 CHAPTER4 TYPE2 PROBLEM3 FREE 00:00:00 MA8353 UNIT1 CHAPTER4 TYPE2 PROBLEM4 FREE 00:00:00 MA8353 UNIT1 CHAPTER4 TYPE3 PROBLEM1 FREE 00:00:00 MA8353 UNIT1 CHAPTER4 TYPE3 PROBLEM2 FREE 00:00:00 MA8353 UNIT1 CHAPTER4 TYPE3 PROBLEM3,4 FREE 00:00:00 MA8353 UNIT1 CHAPTER4 TYPE3 PROBLEM5 FREE 00:00:00 MA8353 UNIT1 CHAPTER4 TYPE3 PROBLEM6 FREE 00:00:00 MA8353 UNIT1 CHAPTER4 TYPE3 PROBLEM7 FREE 00:00:00 MA8353 UNIT1 CHAPTER4 TYPE4 PROBLEM1 FREE 00:00:00 MA8353 UNIT1 CHAPTER4 TYPE4 PROBLEM2 FREE 00:00:00 MA8353 UNIT1 CHAPTER5 NON HOMOGENEOUS LINEAR EQUATION INTRODUCTION FREE 00:00:00 MA8353 UNIT1 CHAPTER5 PROBLEM1,2,3 FREE 00:00:00 MA8353 UNIT1 CHAPTER5 PROBLEM4,5 FREE 00:00:00 UNIT 2 MA8353 UNIT2 INTRODUCTION FREE 00:00:00 MA8353 UNIT2 CHAPTER1 PERIODIC FUNCTION – INTRODUCTION FREE 00:00:00 MA8353 UNIT2 CHAPTER1 DIRICHLET CONDITION FREE 00:00:00 MA8353 UNIT2 CHAPTER1 PROBLEM BASED ON INTERVAL (0,2π) PROBLEM1 FREE 00:00:00 MA8353 UNIT2 CHAPTER1 PROBLEM BASED ON INTERVAL (0,2π) PROBLEM2 FREE 00:00:00 MA8353 UNIT2 CHAPTER1 PROBLEM BASED ON INTERVAL (0,2π) PROBLEM3 FREE 00:00:00 MA8353 UNIT2 CHAPTER1 PROBLEM BASED ON INTERVAL (0,2π) PROBLEM4 FREE 00:00:00 MA8353 UNIT2 CHAPTER1 PROBLEM BASED ON INTERVAL (0,2π) PROBLEM5 FREE 00:00:00 MA8353 UNIT2 CHAPTER1 PROBLEM BASED ON INTERVAL (0,2π) PROBLEM6,7 FREE 00:00:00 MA8353 UNIT2 CHAPTER1 PROBLEM BASED ON INTERVAL (0,2l) PROBLEM1 FREE 00:00:00 MA8353 UNIT2 CHAPTER1 PROBLEM BASED ON INTERVAL (0,2l) PROBLEM2,3 FREE 00:00:00 MA8353 UNIT2 CHAPTER1 PARSEVAL’S IDENTITY FREE 00:00:00 MA8353 UNIT2 CHAPTER2 PROBLEM BASED ON INTERVAL (-π,π) PROBLEM1 FREE 00:00:00 MA8353 UNIT2 CHAPTER2 PROBLEM BASED ON INTERVAL (-π,π) PROBLEM2 FREE 00:00:00 MA8353 UNIT2 CHAPTER2 PROBLEM BASED ON INTERVAL (-π,π) PROBLEM3 FREE 00:00:00 MA8353 UNIT2 CHAPTER2 PROBLEM BASED ON INTERVAL (-π,π) PROBLEM4 FREE 00:00:00 MA8353 UNIT2 CHAPTER2 PROBLEM BASED ON INTERVAL (-π,π) PROBLEM5 FREE 00:00:00 MA8353 UNIT2 –CHAPTER2 PROBLEM BASED ON INTERVAL (-l,l) PROBLEM1 FREE 00:00:00 MA8353 UNIT2 CHAPTER2 PROBLEM BASED ON INTERVAL (-l,l) PROBLEM2 FREE 00:00:00 MA8353 UNIT2 –CHAPTER3 EVEN & ODD FUNCTION PROBLEM1 FREE 00:00:00 MA8353 UNIT2 CHAPTER3 EVEN & ODD FUNCTION PROBLEM2 FREE 00:00:00 MA8353 UNIT2 CHAPTER3 EVEN & ODD FUNCTION PROBLEM3 FREE 00:00:00 MA8353 UNIT2 CHAPTER3 EVEN & ODD FUNCTION PROBLEM4 FREE 00:00:00 MA8353 UNIT2 CHAPTER3 EVEN & ODD FUNCTION PROBLEM5 FREE 00:00:00 MA8353 UNIT2 CHAPTER3 EVEN & ODD FUNCTION PROBLEM6 FREE 00:00:00 MA8353 UNIT2 CHAPTER3 EVEN & ODD FUNCTION (-l,l) PROBLEM1 FREE 00:00:00 MA8353 UNIT2 CHAPTER3 EVEN & ODD FUNCTION (-l,l) PROBLEM2 FREE 00:00:00 MA8353 UNIT2 CHAPTER4 HALF RANGE EXPANSIONS (0,π) PROBLEM1 FREE 00:00:00 MA8353 UNIT2 CHAPTER4 HALF RANGE EXPANSIONS (0,π) PROBLEM2 FREE 00:00:00 MA8353 UNIT2 CHAPTER4 HALF RANGE EXPANSIONS (0,π) PROBLEM3 FREE 00:00:00 MA8353 UNIT2 CHAPTER4 HALF RANGE EXPANSIONS (0,π) PROBLEM4 FREE 00:00:00 MA8353 UNIT2 CHAPTER4 HALF RANGE EXPANSIONS (0,π) PROBLEM5 FREE 00:00:00 MA8353 UNIT2 CHAPTER4 HALF RANGE EXPANSIONS (0,π) PROBLEM6 FREE 00:00:00 MA8353 UNIT2 CHAPTER4 HALF RANGE EXPANSIONS (0,l) PROBLEM1 FREE 00:00:00 MA8353 UNIT2 CHAPTER4 HALF RANGE EXPANSIONS (0,l) PROBLEM2 FREE 00:00:00 MA8353 UNIT2 CHAPTER4 HALF RANGE EXPANSIONS (0,l) PROBLEM3 FREE 00:00:00 MA8353 UNIT2 CHAPTER4 HALF RANGE EXPANSIONS (0,l) PROBLEM4 FREE 00:00:00 MA8353 UNIT2 CHAPTER4 HALF RANGE EXPANSIONS (0,l) PROBLEM5 FREE 00:00:00 MA8353 UNIT2 CHAPTER4 HALF RANGE EXPANSIONS (0,l) PROBLEM6,7 FREE 00:00:00 MA8353 UNIT2 CHAPTER5 COMPLEX FORM PROBLEM1 FREE 00:00:00 MA8353 UNIT2 CHAPTER5 COMPLEX FORM PROBLEM2 FREE 00:00:00 MA8353 UNIT2 CHAPTER5 COMPLEX FORM PROBLEM3 FREE 00:00:00 MA8353 UNIT2 CHAPTER5 COMPLEX FORM PROBLEM4 FREE 00:00:00 MA8353 UNIT2 CHAPTER5 ROOT MEAN SQUARE VALUE PROBLEM1,2 FREE 00:00:00 MA8353 UNIT2 CHAPTER6 HARMONIC ANALYSIS PROBLEM1 FREE 00:00:00 MA8353 UNIT2 CHAPTER6 HARMONIC ANALYSIS PROBLEM2 FREE 00:00:00 MA8353 UNIT2 CHAPTER6 HARMONIC ANALYSIS PROBLEM3 FREE 00:00:00 MA8353 UNIT2 CHAPTER6 HARMONIC ANALYSIS PROBLEM4 FREE 00:00:00 UNIT 3 MA8353 UNIT3 CHAPTER1 CLASSIFICATION OF LINEAR PARTIAL DIFFERENTIAL EQUATION OF SECOND ORDER PROBLEM1 FREE 00:00:00 MA8353 UNIT3 CHAPTER1 CLASSIFICATION OF LINEAR PARTIAL DIFFERENTIAL EQUATION OF SECOND ORDER PROBLEM2,3,4 FREE 00:00:00 MA8353 UNIT3 CHAPTER1 METHOD OF SEPARATION OF VARIABLES AND PROBLEM1 FREE 00:00:00 MA8353 UNIT3 CHAPTER1 METHOD OF SEPARATION OF VARIABLES AND PROBLEM2 FREE 00:00:00 MA8353 UNIT3 CHAPTER2 SOLUTION OF ONE DIMENSIONAL WARE EQUATION TYPE1 INTRODUCTION FREE 00:00:00 MA8353 UNIT3 CHAPTER2 SOLUTION OF ONE DIMENSIONAL WARE EQUATION TYPE1 PROBLEM1 FREE 00:00:00 MA8353 UNIT3 CHAPTER2 SOLUTION OF ONE DIMENSIONAL WARE EQUATION TYPE1 PROBLEM2 FREE 00:00:00 MA8353 UNIT3 CHAPTER2 SOLUTION OF ONE DIMENSIONAL WARE EQUATION TYPE1 PROBLEM3 FREE 00:00:00 MA8353 UNIT3 CHAPTER2 SOLUTION OF ONE DIMENSIONAL WARE EQUATION TYPE1 PROBLEM4 FREE 00:00:00 MA8353 UNIT3 CHAPTER2 SOLUTION OF ONE DIMENSIONAL WARE EQUATION TYPE1 PROBLEM5 FREE 00:00:00 MA8353 UNIT3 CHAPTER2 SOLUTION OF ONE DIMENSIONAL WARE EQUATION TYPE1 PROBLEM6 FREE 00:00:00 MA8353 UNIT3 CHAPTER2 TYPE2 STRING WITH VELOCITY INTRODUCTION FREE 00:00:00 MA8353 UNIT3 CHAPTER2 TYPE2 STRING WITH VELOCITY PROBLEM1 FREE 00:00:00 MA8353 UNIT3 CHAPTER2 TYPE2 STRING WITH VELOCITY PROBLEM2 FREE 00:00:00 MA8353 UNIT3 CHAPTER2 TYPE2 STRING WITH VELOCITY PROBLEM3 FREE 00:00:00 MA8353 UNIT3 CHAPTER3 ONE DIMENSIONAL HEAT FLOW INTRODUCTION PROBLEM1 FREE 00:00:00 MA8353 UNIT3 CHAPTER3 ONE DIMENSIONAL HEAT FLOW INTRODUCTION PROBLEM2 FREE 00:00:00 MA8353 UNIT3 CHAPTER3 STEADY STATE CONDITION & ZERO BOUNDARY CONDITION INTRODUCTION PROBLEM1 FREE 00:00:00 MA8353 UNIT3 CHAPTER3 TEMPERATURE GRADIENT & THERMALLY INSULTED ENDS PROBLEM1 FREE 00:00:00 MA8353 UNIT3 CHAPTER3 TEMPERATURE GRADIENT & THERMALLY INSULTED ENDS PROBLEM2 FREE 00:00:00 MA8353 UNIT3 CHAPTER4 TWO DIMENSIONAL HEAT FLOW EQUATION PROBLEM1 FREE 00:00:00 MA8353 UNIT3 CHAPTER4 TWO DIMENSIONAL HEAT FLOW EQUATION PROBLEM2 , RECTANGULAR PLATES TEMPERATURE GIVEN IN HORIZONTAL EDGE PROBLEM1 FREE 00:00:00 MA8353 UNIT3 CHAPTER4 INFINITE PLATES VERTICLE PLATES PROBLEM2 FREE 00:00:00 MA8353 UNIT3 CHAPTER4 INFINITE PLATES VERTICLE PLATES PROBLEM3 FREE 00:00:00 MA8353 UNIT3 CHAPTER4 INFINITE PLATES VERTICLE PLATES PROBLEM4 FREE 00:00:00 MA8353 UNIT3 TWO MARK PROBLEM 1 TO 6 FREE 00:00:00 UNIT 4 MA8353 UNIT4 INTRODUCTION FREE 00:00:00 MA8353 UNIT4 CHAPTER1 FOURIER TRANSFORM STATEMENT OF FOURIER INTEGRAL THEOREM DEFINITION PROPERTY1,2 FREE 00:00:00 MA8353 UNIT4 CHAPTER1 FOURIER TRANSFORM STATEMENT OF FOURIER INTEGRAL THEOREM DEFINITION PROPERTY3 FREE 00:00:00 MA8353 UNIT4 CHAPTER1 FOURIER TRANSFORM STATEMENT OF FOURIER INTEGRAL THEOREM DEFINITION PROPERTY4,5,6,7,8,9 CONVOLUTION THEOREM FREE 00:00:00 MA8353 UNIT4 CHAPTER1 STATEMENT & PROVE CONVOLUTION THEOREM & PARSEVAL’S IDENTITY FOR FOURIER TRANSFORM FREE 00:00:00 MA8353 UNIT4 CHAPTER2 PROBLEM1,2 FREE 00:00:00 MA8353 UNIT4 CHAPTER2 PROBLEM3 FREE 00:00:00 MA8353 UNIT4 CHAPTER2 PROBLEM4 FREE 00:00:00 MA8353 UNIT4 CHAPTER2 PROBLEM5 FREE 00:00:00 MA8353 UNIT4 CHAPTER2 PROBLEM6 FREE 00:00:00 MA8353 UNIT4 CHAPTER2 PROBLEM7 FREE 00:00:00 MA8353 UNIT4 CHAPTER2 PROBLEM8 FREE 00:00:00 MA8353 UNIT4 CHAPTER2 PROBLEM9 FREE 00:00:00 MA8353 UNIT4 CHAPTER2 PROBLEM10 FREE 00:00:00 MA8353 UNIT4 CHAPTER2 PROBLEM11 & DEFINITION FREE 00:00:00 MA8353 UNIT4 CHAPTER3 FORMULA & PROBLEM1 FREE 00:00:00 MA8353 UNIT4 CHAPTER3 PROBLEM2,3 FREE 00:00:00 MA8353 UNIT4 CHAPTER3 PROBLEM4,5 FREE 00:00:00 MA8353 UNIT4 CHAPTER3 PROBLEM6,7 FREE 00:00:00 MA8353 UNIT4 CHAPTER3 PROBLEM8 FREE 00:00:00 MA8353 UNIT4 CHAPTER3 PROBLEM9 FREE 00:00:00 MA8353 UNIT4 CHAPTER3 PROBLEM10 FREE 00:00:00 MA8353 UNIT4 CHAPTER3 PROBLEM11 FREE 00:00:00 MA8353 UNIT4 CHAPTER3 PROBLEM12 FREE 00:00:00 MA8353 UNIT4 CHAPTER3 PROBLEM13 FREE 00:00:00 MA8353 UNIT4 CHAPTER3 PROBLEM14,15 FREE 00:00:00 MA8353 UNIT4 CHAPTER3 PROBLEM16,17 FREE 00:00:00 MA8353 UNIT4 CHAPTER4 EVALUATION OF INTEGRALS & FORMULAS & PROBLEM1,2 FREE 00:00:00 MA8353 UNIT4 CHAPTER4 EVALUATION OF INTEGRALS & FORMULAS & PROBLEM3,4 FREE 00:00:00 MA8353 UNIT4 CHAPTER4 EVALUATION OF INTEGRALS & FORMULAS & PROBLEM5 FREE 00:00:00 MA8353 UNIT4 CHAPTER4 EVALUATION OF INTEGRALS & FORMULAS & PROBLEM6,7,8 FREE 00:00:00 UNIT 5 MA8353 UNIT5 INTRODUCTION FREE 00:00:00 MA8353 UNIT5 CHAPTER1 Z-TRANSFORM DEFINITION FREE 00:00:00 MA8353 UNIT5 CHAPTER1 Z TRANSFORM PROBLEM1 FREE 00:00:00 MA8353 UNIT5 CHAPTER1 Z TRANSFORM PROBLEM2 FREE 00:00:00 MA8353 UNIT5 CHAPTER1 Z TRANSFORM PROBLEM3 FREE 00:00:00 MA8353 UNIT5 CHAPTER1 Z TRANSFORM PROBLEM4 FREE 00:00:00 MA8353 UNIT5 CHAPTER1 Z TRANSFORM PROBLEM5 FREE 00:00:00 MA8353 UNIT5 CHAPTER1 Z TRANSFORM PROBLEM6 FREE 00:00:00 MA8353 UNIT5 CHAPTER1 Z TRANSFORM PROBLEM7 FREE 00:00:00 MA8353 UNIT5 CHAPTER1 Z TRANSFORM PROBLEM8 FREE 00:00:00 MA8353 UNIT5 CHAPTER1 Z TRANSFORM PROBLEM9 FREE 00:00:00 MA8353 UNIT5 CHAPTER1 Z TRANSFORM PROBLEM10 FREE 00:00:00 MA8353 UNIT5 CHAPTER1 Z TRANSFORM PROBLEM11 FREE 00:00:00 MA8353 UNIT5 CHAPTER1 Z TRANSFORM PROBLEM12 FREE 00:00:00 MA8353 UNIT5 CHAPTER1 Z TRANSFORM PROBLEM13 FREE 00:00:00 MA8353 UNIT5 CHAPTER2 Z TRANSFORM FOR DISCRETE VALUE OF T PROBLEM1 FREE 00:00:00 MA8353 UNIT5 CHAPTER2 Z TRANSFORM FOR DISCRETE VALUE OF T PROBLEM2 FREE 00:00:00 MA8353 UNIT5 CHAPTER2 Z TRANSFORM FOR DISCRETE VALUE OF T PROPERTY1 PROBLEM3 FREE 00:00:00 MA8353 UNIT5 CHAPTER2 Z TRANSFORM FOR DISCRETE VALUE OF T PROPERTY1 PROBLEM4 FREE 00:00:00 MA8353 UNIT5 CHAPTER2 Z TRANSFORM FOR DISCRETE VALUE OF T PROPERTY2 PROBLEM5 FREE 00:00:00 MA8353 UNIT5 CHAPTER2 Z TRANSFORM FOR DISCRETE VALUE OF T PROPERTY2 PROBLEM6 FREE 00:00:00 MA8353 UNIT5 CHAPTER2 Z TRANSFORM FOR DISCRETE VALUE OF T PROPERTY3 PROBLEM7 FREE 00:00:00 MA8353 UNIT5 CHAPTER2 Z TRANSFORM FOR DISCRETE VALUE OF T PROPERTY3 PROBLEM8 FREE 00:00:00 MA8353 UNIT5 CHAPTER2 Z TRANSFORM FOR DISCRETE VALUE OF T PROPERTY3 PROBLEM9 FREE 00:00:00 MA8353 UNIT5 CHAPTER2 PROPERTY 4 INITIAL VALUE THEOREM & FINAL VALUE THEOREM FREE 00:00:00 MA8353 UNIT5 CHAPTER3 INVERSE Z-TRANSFORM FREE 00:00:00 MA8353 UNIT5 CHAPTER3 PARTIAL FRACTION METHOD PROBLEM1 FREE 00:00:00 MA8353 UNIT5 CHAPTER3 PARTIAL FRACTION METHOD PROBLEM2 FREE 00:00:00 MA8353 UNIT5 CHAPTER3 PARTIAL FRACTION METHOD PROBLEM3 FREE 00:00:00 MA8353 UNIT5 CHAPTER3 PARTIAL FRACTION METHOD PROBLEM4 FREE 00:00:00 MA8353 UNIT5 CHAPTER4 RESIDUE METHOD FORMULA FREE 00:00:00 MA8353 UNIT5 CHAPTER4 RESIDUE METHOD PROBLEM1 FREE 00:00:00 MA8353 UNIT5 CHAPTER4 RESIDUE METHOD PROBLEM2 FREE 00:00:00 MA8353 UNIT5 CHAPTER4 RESIDUE METHOD PROBLEM3 FREE 00:00:00 MA8353 UNIT5 CHAPTER4 RESIDUE METHOD PROBLEM4 FREE 00:00:00 MA8353 UNIT5 CHAPTER4 RESIDUE METHOD PROBLEM5 FREE 00:00:00 MA8353 UNIT5 CHAPTER5 CONVOLUTION THEOREM PROBLEM1 FREE 00:00:00 MA8353 UNIT5 CHAPTER5 CONVOLUTION THEOREM PROBLEM2,3 FREE 00:00:00 MA8353 UNIT5 CHAPTER5 CONVOLUTION THEOREM PROBLEM4,5 FREE 00:00:00 MA8353 UNIT5 CHAPTER5 CONVOLUTION THEOREM PROBLEM6 FREE 00:00:00 MA8353 UNIT5 CHAPTER6 FORMATION OF DIFFERENCE EQUATION PROBLEM1,2 FREE 00:00:00 MA8353 UNIT5 CHAPTER6 SOLVING OF DIFFERENCE EQUATION USING Z-TRANSFORM FORMULA PROBLEM1 FREE 00:00:00 MA8353 UNIT5 CHAPTER6 SOLVING OF DIFFERENCE EQUATION USING Z-TRANSFORM PROBLEM2 FREE 00:00:00 MA8353 UNIT5 CHAPTER6 SOLVING OF DIFFERENCE EQUATION USING Z-TRANSFORM PROBLEM3 FREE 00:00:00 MA8353 UNIT5 CHAPTER6 SOLVING OF DIFFERENCE EQUATION USING Z-TRANSFORM PROBLEM4,5 FREE 00:00:00

## N.A

ratings
• 5 stars0
• 4 stars0
• 3 stars0
• 2 stars0
• 1 stars0

No Reviews found for this course.

2576 STUDENTS ENROLLED
• • • • • • • • • • 66659
© BANDHE LEARNENGG SOLUTIONS PRIVATE LIMITED