TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

Slides:

Advertisements

Similar presentations

Signals and Fourier Theory

Advertisements

MATHEMATICAL METHODS. CONTENTS Matrices and Linear systems of equations Eigen values and eigen vectors Real and complex matrices and Quadratic forms Algebraic.

MATHEMATICAL METHODS. CONTENTS Matrices and Linear systems of equations Eigen values and eigen vectors Real and complex matrices and Quadratic forms Algebraic.

PA214 Waves and Fields Fourier Methods Blue book New chapter 12 Fourier sine series Application to the wave equation Fourier cosine series Fourier full.

[YEAR OF ESTABLISHMENT – 1997]

DEPARTMENT OF MATHEMATI CS [ YEAR OF ESTABLISHMENT – 1997 ] DEPARTMENT OF MATHEMATICS, CVRCE.

MATHEMATICAL METHODS. CONTENTS Matrices and Linear systems of equations Eigen values and eigen vectors Real and complex matrices and Quadratic forms Algebraic.

Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Fourier Series & Integrals Text Chapter.

1 The Mathematics of Signal Processing - an Innovative Approach Peter Driessen Faculty of Engineering University of Victoria.

Digital Control Systems The z-Transform. The z Transform Definition of z-Transform The z transform method is an operational method that is very powerful.

DEPARTMENT OF MATHEMATI CS [ YEAR OF ESTABLISHMENT – 1997 ] DEPARTMENT OF MATHEMATICS, CVRCE.

PA214 Waves and Fields Fourier Methods Blue book New chapter 12 Fourier sine series Application to the wave equation Fourier cosine series Fourier full.

DEPARTMENT OF MATHEMATI CS [ YEAR OF ESTABLISHMENT – 1997 ] DEPARTMENT OF MATHEMATICS, CVRCE.

DEPARTMENT OF MATHEMATI CS [ YEAR OF ESTABLISHMENT – 1997 ] DEPARTMENT OF MATHEMATICS, CVRCE.

DEPARTMENT OF MATHEMATI CS [ YEAR OF ESTABLISHMENT – 1997 ] DEPARTMENT OF MATHEMATICS, CVRCE.

Introduction 1. MSc (1994): Punjab University Specialization: Applied Mathematics 2. MS /M.Phil (2006): COMSATS, Islamabad Specialization: Applied Mathematics.

MATHEMATICAL METHODS. CONTENTS Matrices and Linear systems of equations Eigen values and eigen vectors Real and complex matrices and Quadratic forms Algebraic.

MATHEMATICS-I. CONTENTS  Ordinary Differential Equations of First Order and First Degree  Linear Differential Equations of Second and Higher Order 

DEPARTMENT OF MATHEMATI CS [ YEAR OF ESTABLISHMENT – 1997 ] DEPARTMENT OF MATHEMATICS, CVRCE.

DEPARTMENT OF MATHEMATI CS [ YEAR OF ESTABLISHMENT – 1997 ] DEPARTMENT OF MATHEMATICS, CVRCE.

-S.SIVARAJA Dept of MATHEMATICS.  N-NUMERICAL  M-METHODS EASY TO LEARN & EASY TO SCORE.

DEPARTMENT OF MATHEMATI CS [ YEAR OF ESTABLISHMENT – 1997 ] DEPARTMENT OF MATHEMATICS, CVRCE.

Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Partial Differential Equations Text Chapter.

Goals For This Class Quickly review of the main results from last class Convolution and Cross-correlation Discrete Fourier Analysis: Important Considerations.

Chapter 7 Fourier Series (Fourier 급수)

ECE 8443 – Pattern Recognition EE 3512 – Signals: Continuous and Discrete Objectives: Linearity Time Shift and Time Reversal Multiplication Integration.

PA214 Waves and Fields Fourier Methods Blue book New chapter 12 Fourier sine series Application to the wave equation Fourier cosine series Fourier full.

Fundamentals of Electric Circuits Chapter 17

(Lecture #08)1 Digital Signal Processing Lecture# 8 Chapter 5.

1 Review of Continuous-Time Fourier Series. 2 Example 3.5 T/2 T1T1 -T/2 -T 1 This periodic signal x(t) repeats every T seconds. x(t)=1, for |t|

381DP321: Digital Signal Processing Last update on August 27, 2014 Doug Young Suh 10/15/2015.

1 Fourier Representations of Signals & Linear Time-Invariant Systems Chapter 3.

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Background Any function that periodically repeats itself.

Advanced Higher Mathematics Methods in Algebra and Calculus Geometry, Proof and Systems of Equations Applications of Algebra and Calculus AH.

Fourier series: Eigenfunction Approach

1 G. Baribaud/AB-BDI Digital Signal Processing March 2003 DISP-2003 The z-transform  The sampling process  The definition and the properties.

Input Function x(t) Output Function y(t) T[ ]. Consider The following Input/Output relations.

Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Engineering Mathematics Lecture 05: 2.

P.VIJAYALAKSHMI M.E(power electronics &drives) Assistant Professor EEE Department.

AIM To impart enough Mathematical background in Matrices and Differential Calculus for the exact understanding of the Engineering subjects.

MATHEMATICS-II SUB.CODE: MA1151.

1 Methods in Image Analysis – Lecture 3 Fourier CMU Robotics Institute U. Pitt Bioengineering 2630 Spring Term, 2004 George Stetten, M.D., Ph.D.

15. Fourier analysis techniques

Differential Equations Linear Equations with Variable Coefficients.

MATHEMATICAL METHODS. CONTENTS Matrices and Linear systems of equations Eigen values and eigen vectors Real and complex matrices and Quadratic forms Algebraic.

Solving Partial Differential Equation Numerically Pertemuan 13 Matakuliah: S0262-Analisis Numerik Tahun: 2010.

HANDLED BY C.KARTHIK LECTURER, ECE DEPARTMENT.  To study and analyse characteristics of continuous, discrete signals and systems.

بسم الله الرحمن الرحيم University of Khartoum Department of Electrical and Electronic Engineering Third Year – 2015 Dr. Iman AbuelMaaly Abdelrahman

بسم الله الرحمن الرحيم Digital Signal Processing Lecture 3 Review of Discerete time Fourier Transform (DTFT) University of Khartoum Department of Electrical.

Fourier analysis Periodic function: Any (“reasonable”) periodic function, can be written as a series of sines and cosines “vibrations”, whose frequencies.

OBJECTIVES Students will able to Students will able to 1. define differential equation 1. define differential equation 2. identify types, order & degree.

Subject : Advance engineering mathematics Topic : Fourier series & Fourier integral.

Chapter 6 Laplace Transform

Integral Transform Method

Advanced Higher Mathematics

Advanced Engineering Mathematics 6th Edition, Concise Edition

First order non linear pde’s

Fourier Series.

Complex Frequency and Laplace Transform

Chapter 15 Introduction to the Laplace Transform

A Presentation on APPLIED MATHEMATICS (9030)

Introduction to Partial Differential Equations

UNIT II Analysis of Continuous Time signal

Second Order-Partial Differential Equations

Continuous-Time Fourier Transform

Signals & Systems (CNET - 221) Chapter-4

4. The Continuous time Fourier Transform

LECTURE 11: FOURIER TRANSFORM PROPERTIES

Presentation transcript:

TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS SUBJECT CODE: MA6351

UNIT 1 PARTIAL DIFFERENTIAL EQUATIONS FORMATION OF P.D.E SINGULAR INTEGRALS SOLUTION OF STANDARD TYPES OF 1ST ORDER P.D.E

LAGRANGE’S LINEAR EQUATION LINEAR P.D.E OF 2ND AND HIGHER ORDER WITH CONSTANT COEFFICIENTS OF BOTH HOMOGENEOUS AND NON HOMOGENEOUS TYPES

applicationS MATHEMATICAL MODELING ANY FIELD INVOLVING ATLEAST AN UNKNOWN FUNCTION

UNIT 2 FOURIER SERIES DRICHLET’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

applicationS ANALYSIS OF CURRENT FLOW IN ELECTRICAL ENGINEERING ANALYSIS OF SOUND WAVES ELECTRONICALLY SYNTHESIZED MUSIC AND TAKING COMPUTER CLIPS

UNIT 3 APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS CLASSIFICATION OF P.D.E 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

UNIT 4 FOURIER TRANSFORMS STATEMENT OF FOURIER INTEGRAL THEOREM FOURIER TRANSFORM PAIR

FOURIER SINE AND COSINE TRANSFORMS PROPERTIES TRANSFORMS OF SIMPLE FUNCTIONS CONVOLUTION THEOREM PARSEVAL’S IDENTITY

applicationS IN THE REPRESENTATION OF ELECTRICAL FIELD DISCUSSION OF THE PHASE CHANGE ASSOCIATED WITH DIFFERENT PATHS IT IS HIGHLY USEFUL IN SIGNAL PROCESSING

UNIT 5 Z-TRANSFORMS Z TRANSFORMS ELEMENTARY PROERTIES INVERSE Z-TRANSFORM USING PARTIAL FRACTION AND RESIDUES

CONVOLUTION THEOREM FORMATION OF DIFFERENTIAL EQUATIONS SOLUTION OF DIFFERENTIAL EQUATIONS USING Z-TRANSFORMS

applicationS IN DIGITAL SIGNAL PROCESSING ANALYSIS OF LINEAR DISCRETE SYSTEM ANALYSIS OF DISCRETE SIGNALS ANALYSIS OF DIGITAL FILTERS SIMULATIONS OF CONTINUOUS SYSTEM

TEXT BOOKS Veerarajan T., "Transforms and Partial Differential Equations", Tata McGraw Hill Education Pvt. Ltd., New Delhi, Second reprint, 2012. Grewal B.S., "Higher Engineering Mathematics", 42nd Edition, Khanna Publishers, Delhi, 2012.

Narayanan S. , Manicavachagom Pillay. T. K and Ramanaiah Narayanan S., Manicavachagom Pillay.T.K and Ramanaiah.G "Advanced Mathematics for Engineering Students" Vol. II & III, S.Viswanathan Publishers Pvt Ltd. 1998.

references Bali. N.P and Manish Goyal, "A Textbook of Engineering Mathematics", 7th Edition, Laxmi Publications Pvt Ltd, 2007. Ramana. B.V., "Higher Engineering Mathematics", Tata McGraw Hill Publishing Company Limited, New Delhi, 2008.

Glyn James, "Advanced Modern Engineering Mathematics", 3rd Edition, Pearson Education, 2007. Erwin Kreyszig, "Advanced Engineering Mathematics", 8th Edition, Wiley India, 2007.

Ray Wylie C and Barrett. L Ray Wylie C and Barrett.L.C, "Advanced Engineering Mathematics" Tata McGraw Hill Education Pvt Ltd, Sixth Edition, New Delhi, 2012. Datta K.B., "Mathematical Methods of Science and Engineering", Cengage Learning India Pvt Ltd, Delhi, 2013.