NUMERICAL METHODS FOR ENGINEERING APPLICATION
|
|
- Martin Preston
- 5 years ago
- Views:
Transcription
1 NUMERICAL METHODS FOR ENGINEERING APPLICATION Second Edition JOEL H. FERZIGER A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York / Chichester / Weinheim / Brisbane / Singapore / Toronto
2 CONTENTS PREFACE TO THE SECOND EDITION PREFACE TO THE FIRST EDITION xi xv 1. SHORT REVIEW OF LINEAR ALGEBRA Introduction and Notation, Gauss Elimination and LU Decomposition, Tridiagonal and Other Banded Systems, Block Systems, Eigenvalues, INTERPOLATION Lagrange Interpolation, Theory, Error Analysis, Divided Differences, Examples, Piecewise Polynomial Interpolation, Summary, Hermite Interpolation, Splines, Definition and Development, Examples and Programs, 32
3 B-Sphnes, Final Remarks, Tension Splines, Parametric and Multidimensional Interpolation Computer Graphics, Parametric Interpolation, Multidimensional Interpolation, Graphics and Design, 40 Problems, 41 INTEGRATION 3.1. Newton-Cotes Formulas, Richardson Extrapolation and Error Estimation, Romberg Integration, Adaptive Quadrature, Gauss Quadrature, Monte Carlo Methods, Singularities, Integration by Parts, Singularity Subtraction, Concluding Remarks, 73 Problems, 73 ORDINARY DIFFERENTIAL EQUATIONS: I. INITIAL VALUE PROBLEMS 4.1. Numerical Differentiation, Interpolation, Taylor Series, Numerical Integration, Nonuniform Grids, Euler Explicit Method, Stability, Backward or Implicit Euler Method, Error Estimation and Accuracy Improvement, Error Estimation, Richardson Extrapolation, Trapezoid Rule, Other Approaches, Predictor-Corrector Methods, 109
4 CONTENTS VII 4.8. Runge-Kutta Methods, Multistep Methods, Choice of Method: Automatic Error Control, Systems of Equations Stiffness, Treatment of Systems of Ordinary Differential Equations, Stiffness, Numerical Methods for Stiff Problems, Splitting Methods, Variable-Step-Size Methods, Inherent Instability, Growing Solutions, 134 Problems, ORDINARY DIFFERENTIAL EQUATIONS: II. BOUNDARY VALUE PROBLEMS Shooting, Direct Methods: Introduction, Higher-Order Direct Methods, Compact Methods, Nonuniform Grids, Finite Difference Approximations, Coordinate Transformations, Finite Element Methods, Adaptive Grids, Eigenvalue Problems, Direct Methods, Shooting Methods, 178 Problems, PARTIAL DIFFERENTIAL EQUATIONS: I. PARABOLIC EQUATIONS Classification of Partial Differential Equations, Characteristics, Explicit Methods, Crank-Nicolson Method, Dufort-Frankel Method, Keller Box Method, Second-Order Backward Method, 207
5 VIII CONTENTS 6.7. Higher-Order Methods, Two and Three Spatial Dimensions: Alternating Direction Implicit Methods, Heat Equation in Two Dimensions, Peaceman-Rachford Method, Approximate Factorization, Other Splitting Methods, Other Coordinate Systems, Nonlinear Problems, Final Remarks Other Methods, 226 Problems, PARTIAL DIFFERENTIAL EQUATIONS: II. ELLIPTIC EQUATIONS Discretization, Finite Differences, Finite Volume Approximations, Boundary Conditions, System of Equations, Complex Geometry, Introduction to Iterative Methods and Their Properties, Construction of Iterative Methods, Errors in Iterative Methods, Convergence Error, Stopping Criterion, Estimation of Discretization Error, Jacobi Iteration, The Method, Convergence, Connection to Heat Equation, Other Equations, Gauss-Seidel Method, Line Relaxation Method, Successive Overrelaxation, Extrapolation, Point Successive Overrelaxation, Successive Line Overrelaxation, Alternating Direction Implicit Methods, 263
6 CONTENTS ix 7.8. Incomplete LU Decomposition: Stone's Method, Methods for Parallel Computers, Red-Black Gauss-Seidel Method, Parallelization of Other Methods, Multigrid Methods, Conjugate Gradient Methods, Concept, Preconditioning, Biconjugate Gradients and CGSTAB, Adaptive Grids, Finite Element Methods, Discrete Fourier Transforms, Review of Fourier Series, Discrete Fourier Series, Spectral Differentiation, Fast Fourier Transform, Fourier or Spectral Methods, Boundary Integral Methods, Finite Differences in Complex Geometry, 311 Problems, PARTIAL DIFFERENTIAL EQUATIONS: III. HYPERBOLIC EQUATIONS Review of Theory, Quasi-Linear First-Order Equations, Characteristics of Second-Order Equations, Nonlinear Equations and Shocks, Method of Characteristics, First-Order Equations, Second-Order Equations, Method of Characteristics on Cartesian Grids, Explicit Methods, Explicit Central Difference Methods, Upwind Methods, Lax-Wendroff Method, Implicit Methods, Splitting Methods, Explicit Split Methods, 353
7 X CONTENTS Convection in Two Dimensions, Implicit Split Methods, 360 Problems, 361 APPENDIX A: LIST OF COMPUTER CODES 363 APPENDIX B: ANNOTATED BIBLIOGRAPHY 366 APPENDIX C: NOTE ON THE NEWTON-RAPHSON METHOD 371 INDEX 373
Numerical Methods for Engineers and Scientists
Numerical Methods for Engineers and Scientists Second Edition Revised and Expanded Joe D. Hoffman Department of Mechanical Engineering Purdue University West Lafayette, Indiana m MARCEL D E К К E R MARCEL
More informationNumerical Analysis. A Comprehensive Introduction. H. R. Schwarz University of Zürich Switzerland. with a contribution by
Numerical Analysis A Comprehensive Introduction H. R. Schwarz University of Zürich Switzerland with a contribution by J. Waldvogel Swiss Federal Institute of Technology, Zürich JOHN WILEY & SONS Chichester
More informationApplied Numerical Analysis
Applied Numerical Analysis Using MATLAB Second Edition Laurene V. Fausett Texas A&M University-Commerce PEARSON Prentice Hall Upper Saddle River, NJ 07458 Contents Preface xi 1 Foundations 1 1.1 Introductory
More informationNumerical Methods. Scientists. Engineers
Third Edition Numerical Methods for Scientists and Engineers K. Sankara Rao Numerical Methods for Scientists and Engineers Numerical Methods for Scientists and Engineers Third Edition K. SANKARA RAO Formerly,
More informationNUMERICAL COMPUTATION IN SCIENCE AND ENGINEERING
NUMERICAL COMPUTATION IN SCIENCE AND ENGINEERING C. Pozrikidis University of California, San Diego New York Oxford OXFORD UNIVERSITY PRESS 1998 CONTENTS Preface ix Pseudocode Language Commands xi 1 Numerical
More informationPreface. 2 Linear Equations and Eigenvalue Problem 22
Contents Preface xv 1 Errors in Computation 1 1.1 Introduction 1 1.2 Floating Point Representation of Number 1 1.3 Binary Numbers 2 1.3.1 Binary number representation in computer 3 1.4 Significant Digits
More informationNUMERICAL MATHEMATICS AND COMPUTING
NUMERICAL MATHEMATICS AND COMPUTING Fourth Edition Ward Cheney David Kincaid The University of Texas at Austin 9 Brooks/Cole Publishing Company I(T)P An International Thomson Publishing Company Pacific
More informationNumerical Methods for Engineers
Numerical Methods for Engineers SEVENTH EDITION Steven C Chopra Berger Chair in Computing and Engineering Tufts University Raymond P. Canal Professor Emeritus of Civil Engineering of Michiaan University
More informationNumerical Methods with MATLAB
Numerical Methods with MATLAB A Resource for Scientists and Engineers G. J. BÖRSE Lehigh University PWS Publishing Company I(T)P AN!NTERNATIONAL THOMSON PUBLISHING COMPANY Boston Albany Bonn Cincinnati
More informationIntroduction to Numerical Analysis
J. Stoer R. Bulirsch Introduction to Numerical Analysis Second Edition Translated by R. Bartels, W. Gautschi, and C. Witzgall With 35 Illustrations Springer Contents Preface to the Second Edition Preface
More informationNumerical Methods for Engineers. and Scientists. Applications using MATLAB. An Introduction with. Vish- Subramaniam. Third Edition. Amos Gilat.
Numerical Methods for Engineers An Introduction with and Scientists Applications using MATLAB Third Edition Amos Gilat Vish- Subramaniam Department of Mechanical Engineering The Ohio State University Wiley
More informationNUMERICAL METHODS USING MATLAB
NUMERICAL METHODS USING MATLAB Dr John Penny George Lindfield Department of Mechanical Engineering, Aston University ELLIS HORWOOD NEW YORK LONDON TORONTO SYDNEY TOKYO SINGAPORE Preface 1 An introduction
More informationIndex. higher order methods, 52 nonlinear, 36 with variable coefficients, 34 Burgers equation, 234 BVP, see boundary value problems
Index A-conjugate directions, 83 A-stability, 171 A( )-stability, 171 absolute error, 243 absolute stability, 149 for systems of equations, 154 absorbing boundary conditions, 228 Adams Bashforth methods,
More informationA THEORETICAL INTRODUCTION TO NUMERICAL ANALYSIS
A THEORETICAL INTRODUCTION TO NUMERICAL ANALYSIS Victor S. Ryaben'kii Semyon V. Tsynkov Chapman &. Hall/CRC Taylor & Francis Group Boca Raton London New York Chapman & Hall/CRC is an imprint of the Taylor
More informationNumerical Mathematics
Alfio Quarteroni Riccardo Sacco Fausto Saleri Numerical Mathematics Second Edition With 135 Figures and 45 Tables 421 Springer Contents Part I Getting Started 1 Foundations of Matrix Analysis 3 1.1 Vector
More informationContents. Preface to the Third Edition (2007) Preface to the Second Edition (1992) Preface to the First Edition (1985) License and Legal Information
Contents Preface to the Third Edition (2007) Preface to the Second Edition (1992) Preface to the First Edition (1985) License and Legal Information xi xiv xvii xix 1 Preliminaries 1 1.0 Introduction.............................
More informationReview. Numerical Methods Lecture 22. Prof. Jinbo Bi CSE, UConn
Review Taylor Series and Error Analysis Roots of Equations Linear Algebraic Equations Optimization Numerical Differentiation and Integration Ordinary Differential Equations Partial Differential Equations
More informationComputational Methods
Numerical Computational Methods Revised Edition P. B. Patil U. P. Verma Alpha Science International Ltd. Oxford, U.K. CONTENTS Preface List ofprograms v vii 1. NUMER1CAL METHOD, ERROR AND ALGORITHM 1 1.1
More informationMATHEMATICAL METHODS INTERPOLATION
MATHEMATICAL METHODS INTERPOLATION I YEAR BTech By Mr Y Prabhaker Reddy Asst Professor of Mathematics Guru Nanak Engineering College Ibrahimpatnam, Hyderabad SYLLABUS OF MATHEMATICAL METHODS (as per JNTU
More informationKINGS COLLEGE OF ENGINEERING DEPARTMENT OF MATHEMATICS ACADEMIC YEAR / EVEN SEMESTER QUESTION BANK
KINGS COLLEGE OF ENGINEERING MA5-NUMERICAL METHODS DEPARTMENT OF MATHEMATICS ACADEMIC YEAR 00-0 / EVEN SEMESTER QUESTION BANK SUBJECT NAME: NUMERICAL METHODS YEAR/SEM: II / IV UNIT - I SOLUTION OF EQUATIONS
More informationTABLE OF CONTENTS INTRODUCTION, APPROXIMATION & ERRORS 1. Chapter Introduction to numerical methods 1 Multiple-choice test 7 Problem set 9
TABLE OF CONTENTS INTRODUCTION, APPROXIMATION & ERRORS 1 Chapter 01.01 Introduction to numerical methods 1 Multiple-choice test 7 Problem set 9 Chapter 01.02 Measuring errors 11 True error 11 Relative
More informationPARTIAL DIFFERENTIAL EQUATIONS
MATHEMATICAL METHODS PARTIAL DIFFERENTIAL EQUATIONS I YEAR B.Tech By Mr. Y. Prabhaker Reddy Asst. Professor of Mathematics Guru Nanak Engineering College Ibrahimpatnam, Hyderabad. SYLLABUS OF MATHEMATICAL
More informationNumerical Solution of partial differential equations
G. D. SMITH Brunei University Numerical Solution of partial differential equations FINITE DIFFERENCE METHODS THIRD EDITION CLARENDON PRESS OXFORD Contents NOTATION 1. INTRODUCTION AND FINITE-DIFFERENCE
More informationFundamental Numerical Methods for Electrical Engineering
Stanislaw Rosloniec Fundamental Numerical Methods for Electrical Engineering 4y Springei Contents Introduction xi 1 Methods for Numerical Solution of Linear Equations 1 1.1 Direct Methods 5 1.1.1 The Gauss
More informationME Computational Fluid Mechanics Lecture 5
ME - 733 Computational Fluid Mechanics Lecture 5 Dr./ Ahmed Nagib Elmekawy Dec. 20, 2018 Elliptic PDEs: Finite Difference Formulation Using central difference formulation, the so called five-point formula
More informationExcel for Scientists and Engineers Numerical Method s. E. Joseph Billo
Excel for Scientists and Engineers Numerical Method s E. Joseph Billo Detailed Table of Contents Preface Acknowledgments About the Author Chapter 1 Introducing Visual Basic for Applications 1 Chapter
More informationNumerical Analysis. Introduction to. Rostam K. Saeed Karwan H.F. Jwamer Faraidun K. Hamasalh
Iraq Kurdistan Region Ministry of Higher Education and Scientific Research University of Sulaimani Faculty of Science and Science Education School of Science Education-Mathematics Department Introduction
More informationPreface to the Second Edition. Preface to the First Edition
n page v Preface to the Second Edition Preface to the First Edition xiii xvii 1 Background in Linear Algebra 1 1.1 Matrices................................. 1 1.2 Square Matrices and Eigenvalues....................
More informationThird Edition. William H. Press. Raymer Chair in Computer Sciences and Integrative Biology The University of Texas at Austin. Saul A.
NUMERICAL RECIPES The Art of Scientific Computing Third Edition William H. Press Raymer Chair in Computer Sciences and Integrative Biology The University of Texas at Austin Saul A. Teukolsky Hans A. Bethe
More informationSOLUTION OF EQUATION AND EIGENVALUE PROBLEMS PART A( 2 MARKS)
CHENDU COLLEGE OF ENGINEERING AND TECHNOLOGY (Approved by AICTE New Delhi, Affiliated to Anna University Chennai. Zamin Endathur Village, Madurntakam Taluk, Kancheepuram Dist.-603311.) MA6459 - NUMERICAL
More informationUnit I (Testing of Hypothesis)
SUBJECT NAME : Statistics and Numerical Methods SUBJECT CODE : MA645 MATERIAL NAME : Part A questions REGULATION : R03 UPDATED ON : November 07 (Upto N/D 07 Q.P) Unit I (Testing of Hypothesis). State level
More informationIntroduction to Numerical Analysis
J. Stoer R. Bulirsch Introduction to Numerical Analysis Translated by R. Bartels, W. Gautschi, and C. Witzgall Springer Science+Business Media, LLC J. Stoer R. Bulirsch Institut fiir Angewandte Mathematik
More informationCAM Ph.D. Qualifying Exam in Numerical Analysis CONTENTS
CAM Ph.D. Qualifying Exam in Numerical Analysis CONTENTS Preliminaries Round-off errors and computer arithmetic, algorithms and convergence Solutions of Equations in One Variable Bisection method, fixed-point
More informationNumerical Methods for Engineers
Numerical Methods for Engineers S EVEN TH ED I TI O N Steven C. Chapra Berger Chair in Computing and Engineering Tufts University Raymond P. Canale Professor Emeritus of Civil Engineering University of
More informationName of the Student: Unit I (Solution of Equations and Eigenvalue Problems)
Engineering Mathematics 8 SUBJECT NAME : Numerical Methods SUBJECT CODE : MA6459 MATERIAL NAME : University Questions REGULATION : R3 UPDATED ON : November 7 (Upto N/D 7 Q.P) (Scan the above Q.R code for
More informationContents. Preface... xi. Introduction...
Contents Preface... xi Introduction... xv Chapter 1. Computer Architectures... 1 1.1. Different types of parallelism... 1 1.1.1. Overlap, concurrency and parallelism... 1 1.1.2. Temporal and spatial parallelism
More informationAPPLIED NUMERICAL LINEAR ALGEBRA
APPLIED NUMERICAL LINEAR ALGEBRA James W. Demmel University of California Berkeley, California Society for Industrial and Applied Mathematics Philadelphia Contents Preface 1 Introduction 1 1.1 Basic Notation
More informationCONTENTS. ABOUTTHEAUTHORS xviii PART ONE MODELING, COMPUTERS, AND ERROR ANALYSIS 3
-- PREFACE xvi ABOUTTHEAUTHORS xviii PART ONE MODELING, COMPUTERS, AND ERROR ANALYSIS 3 PT1. 1 Motivation 3 PT1.2 Mathematical Background 5 PT1.3 Orientation 8 CHAPTER 1 Mathematical Modeling and Engineering
More informationContents. I Basic Methods 13
Preface xiii 1 Introduction 1 I Basic Methods 13 2 Convergent and Divergent Series 15 2.1 Introduction... 15 2.1.1 Power series: First steps... 15 2.1.2 Further practical aspects... 17 2.2 Differential
More informationNUMERICAL METHODS. lor CHEMICAL ENGINEERS. Using Excel', VBA, and MATLAB* VICTOR J. LAW. CRC Press. Taylor & Francis Group
NUMERICAL METHODS lor CHEMICAL ENGINEERS Using Excel', VBA, and MATLAB* VICTOR J. LAW CRC Press Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Croup,
More informationNotes on Numerical Analysis
Notes on Numerical Analysis Alejandro Cantarero This set of notes covers topics that most commonly show up on the Numerical Analysis qualifying exam in the Mathematics department at UCLA. Each section
More informationLECTURES IN BASIC COMPUTATIONAL NUMERICAL ANALYSIS
Ax = b Z b a " 1 f(x) dx = h 2 (f X 1 + f n )+ f i #+ O(h 2 ) n 1 i=2 LECTURES IN BASIC COMPUTATIONAL NUMERICAL ANALYSIS x (m+1) = x (m) J(x (m) ) 1 F (x (m) ) p n (x) = X n+1 i=1 " n+1 Y j=1 j6=i # (x
More informationPartial Differential Equations with Numerical Methods
Stig Larsson Vidar Thomée Partial Differential Equations with Numerical Methods May 2, 2003 Springer Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Tokyo Preface Our purpose in this
More informationNumerical Analysis for Engineers and Scientists
Numerical Analysis for Engineers and Scientists Striking a balance between theory and practice, this graduate-level text is perfect for students in the applied sciences. The author provides a clear introduction
More information2.29 Numerical Fluid Mechanics Spring 2015 Lecture 9
Spring 2015 Lecture 9 REVIEW Lecture 8: Direct Methods for solving (linear) algebraic equations Gauss Elimination LU decomposition/factorization Error Analysis for Linear Systems and Condition Numbers
More informationIntroduction. Finite and Spectral Element Methods Using MATLAB. Second Edition. C. Pozrikidis. University of Massachusetts Amherst, USA
Introduction to Finite and Spectral Element Methods Using MATLAB Second Edition C. Pozrikidis University of Massachusetts Amherst, USA (g) CRC Press Taylor & Francis Group Boca Raton London New York CRC
More informationNUMERICAL ANALYSIS SYLLABUS MATHEMATICS PAPER IV (A)
NUMERICAL ANALYSIS SYLLABUS MATHEMATICS PAPER IV (A) Unit - 1 Errors & Their Accuracy Solutions of Algebraic and Transcendental Equations Bisection Method The method of false position The iteration method
More informationComputer Simulation Using Particles
Computer Simulation Using Particles R W Hockney Emeritus Professor, University ofreading and J W Eastwood Culham Laboratory, Abingdon Institute of Physics Publishing Bristol and Philadelphia CONTENTS Foreword
More informationBASIC EXAM ADVANCED CALCULUS/LINEAR ALGEBRA
1 BASIC EXAM ADVANCED CALCULUS/LINEAR ALGEBRA This part of the Basic Exam covers topics at the undergraduate level, most of which might be encountered in courses here such as Math 233, 235, 425, 523, 545.
More informationNumerical Analysis Solution of Algebraic Equation (non-linear equation) 1- Trial and Error. 2- Fixed point
Numerical Analysis Solution of Algebraic Equation (non-linear equation) 1- Trial and Error In this method we assume initial value of x, and substitute in the equation. Then modify x and continue till we
More informationNumerical Recipes. in Fortran 77. The Art of Scientific Computing Second Edition. Volume 1 of Fortran Numerical Recipes. William H.
Numerical Recipes in Fortran 77 The Art of Scientific Computing Second Edition Volume 1 of Fortran Numerical Recipes William H. Press Harvard-Smithsonian Center for Astrophysics Saul A. Teukolsky Department
More informationComputation Fluid Dynamics
Computation Fluid Dynamics CFD I Jitesh Gajjar Maths Dept Manchester University Computation Fluid Dynamics p.1/189 Garbage In, Garbage Out We will begin with a discussion of errors. Useful to understand
More informationAppendix A Computer Programs on the Accompanying CD-ROM
Appendix A Computer Programs on the Accompanying CD-ROM The CD-ROM accompanying this book contains both source and executable computer programs and test cases. They are listed below. Prior to running the
More informationAdvanced. Engineering Mathematics
Advanced Engineering Mathematics A new edition of Further Engineering Mathematics K. A. Stroud Formerly Principal Lecturer Department of Mathematics, Coventry University with additions by Dexter j. Booth
More informationMATHEMATICS. Course Syllabus. Section A: Linear Algebra. Subject Code: MA. Course Structure. Ordinary Differential Equations
MATHEMATICS Subject Code: MA Course Structure Sections/Units Section A Section B Section C Linear Algebra Complex Analysis Real Analysis Topics Section D Section E Section F Section G Section H Section
More informationReview for Exam 2 Ben Wang and Mark Styczynski
Review for Exam Ben Wang and Mark Styczynski This is a rough approximation of what we went over in the review session. This is actually more detailed in portions than what we went over. Also, please note
More informationMath 411 Preliminaries
Math 411 Preliminaries Provide a list of preliminary vocabulary and concepts Preliminary Basic Netwon's method, Taylor series expansion (for single and multiple variables), Eigenvalue, Eigenvector, Vector
More informationOPEN CHANNEL FLOW. Computer Applications. Numerical Methods and. Roland Jeppson. CRC Press UNIVERSITATSB'BUOTHEK TECHNISCHE. INFORMATlONSBiBUOTHEK
OPEN CHANNEL FLOW Numerical Methods and Computer Applications Roland Jeppson TECHNISCHE INFORMATlONSBiBUOTHEK UNIVERSITATSB'BUOTHEK HANNOVER Si. i. CRC Press Taylor &.Francis Group Boca Raton London New
More informationVirtual University of Pakistan
Virtual University of Pakistan File Version v.0.0 Prepared For: Final Term Note: Use Table Of Content to view the Topics, In PDF(Portable Document Format) format, you can check Bookmarks menu Disclaimer:
More informationFourth Order RK-Method
Fourth Order RK-Method The most commonly used method is Runge-Kutta fourth order method. The fourth order RK-method is y i+1 = y i + 1 6 (k 1 + 2k 2 + 2k 3 + k 4 ), Ordinary Differential Equations (ODE)
More informationTHE NUMERICAL TREATMENT OF DIFFERENTIAL EQUATIONS
THE NUMERICAL TREATMENT OF DIFFERENTIAL EQUATIONS 2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. BY DR. LOTHAR COLLATZ
More informationExact and Approximate Numbers:
Eact and Approimate Numbers: The numbers that arise in technical applications are better described as eact numbers because there is not the sort of uncertainty in their values that was described above.
More informationIntroduction to Applied Linear Algebra with MATLAB
Sigam Series in Applied Mathematics Volume 7 Rizwan Butt Introduction to Applied Linear Algebra with MATLAB Heldermann Verlag Contents Number Systems and Errors 1 1.1 Introduction 1 1.2 Number Representation
More informationITERATIVE METHODS FOR SPARSE LINEAR SYSTEMS
ITERATIVE METHODS FOR SPARSE LINEAR SYSTEMS YOUSEF SAAD University of Minnesota PWS PUBLISHING COMPANY I(T)P An International Thomson Publishing Company BOSTON ALBANY BONN CINCINNATI DETROIT LONDON MADRID
More informationENGINEERING MATHEMATICS I. CODE: 10 MAT 11 IA Marks: 25 Hrs/Week: 04 Exam Hrs: 03 PART-A
ENGINEERING MATHEMATICS I CODE: 10 MAT 11 IA Marks: 25 Hrs/Week: 04 Exam Hrs: 03 Total Hrs: 52 Exam Marks:100 PART-A Unit-I: DIFFERENTIAL CALCULUS - 1 Determination of n th derivative of standard functions-illustrative
More informationAPPLIED FUNCTIONAL ANALYSIS
APPLIED FUNCTIONAL ANALYSIS Second Edition JEAN-PIERRE AUBIN University of Paris-Dauphine Exercises by BERNARD CORNET and JEAN-MICHEL LASRY Translated by CAROLE LABROUSSE A Wiley-Interscience Publication
More informationIndex. C 2 ( ), 447 C k [a,b], 37 C0 ( ), 618 ( ), 447 CD 2 CN 2
Index advection equation, 29 in three dimensions, 446 advection-diffusion equation, 31 aluminum, 200 angle between two vectors, 58 area integral, 439 automatic step control, 119 back substitution, 604
More informationAN INTRODUCTION TO THE FRACTIONAL CALCULUS AND FRACTIONAL DIFFERENTIAL EQUATIONS
AN INTRODUCTION TO THE FRACTIONAL CALCULUS AND FRACTIONAL DIFFERENTIAL EQUATIONS KENNETH S. MILLER Mathematical Consultant Formerly Professor of Mathematics New York University BERTRAM ROSS University
More information1 Number Systems and Errors 1
Contents 1 Number Systems and Errors 1 1.1 Introduction................................ 1 1.2 Number Representation and Base of Numbers............. 1 1.2.1 Normalized Floating-point Representation...........
More informationPartial Differential Equations and the Finite Element Method
Partial Differential Equations and the Finite Element Method Pavel Solin The University of Texas at El Paso Academy of Sciences ofthe Czech Republic iwiley- INTERSCIENCE A JOHN WILEY & SONS, INC, PUBLICATION
More informationKernel-based Approximation. Methods using MATLAB. Gregory Fasshauer. Interdisciplinary Mathematical Sciences. Michael McCourt.
SINGAPORE SHANGHAI Vol TAIPEI - Interdisciplinary Mathematical Sciences 19 Kernel-based Approximation Methods using MATLAB Gregory Fasshauer Illinois Institute of Technology, USA Michael McCourt University
More information(f(x) P 3 (x)) dx. (a) The Lagrange formula for the error is given by
1. QUESTION (a) Given a nth degree Taylor polynomial P n (x) of a function f(x), expanded about x = x 0, write down the Lagrange formula for the truncation error, carefully defining all its elements. How
More informationNumerical Recipes in C visit
Numerical Recipes in C visit The Art of Scientific Computing Second Edition William H. Press Harvard-Smithsonian Center for Astrophysics Saul A. Teukolsky Department of Physics, Cornell University William
More informationNumerical Cornp u tat ion
Numerical Cornp u tat ion n INTERNAL AND EXTERNAL FLOWS Volume 1 : Fundamentals of Numerical Discretization Charles Hirsch Department of Fluid Mechanics, Vrije Universiteit Brussel, Brussels, Belgium A
More informationSyllabus of Numerical Analysis of Different Universities Introduction to Numerical Analysis
Syllabus of Numerical Analysis of Different Universities In this appendix we give the syllabus for the courses of numerical analysis held in different universities of USA, UK, Saudi Arabia, and others.
More informationNumerical Analysis. Elements of. Second Edition. Radhey S. Gupta
Elements of Numerical Analysis Second Edition Cambridge House, 4381/4 Ansari Road, Daryaganj, Delhi 110002, India Cambridge University Press is part of the University of Cambridge. It furthers the University
More informationTable 1 Principle Matlab operators and functions Name Description Page reference
Matlab Index Table 1 summarises the Matlab supplied operators and functions to which we have referred. In most cases only a few of the options available to the individual functions have been fully utilised.
More informationComputational Fluid Dynamics-1(CFDI)
بسمه تعالی درس دینامیک سیالات محاسباتی 1 دوره کارشناسی ارشد دانشکده مهندسی مکانیک دانشگاه صنعتی خواجه نصیر الدین طوسی Computational Fluid Dynamics-1(CFDI) Course outlines: Part I A brief introduction to
More informationADVANCED ENGINEERING MATHEMATICS
ADVANCED ENGINEERING MATHEMATICS DENNIS G. ZILL Loyola Marymount University MICHAEL R. CULLEN Loyola Marymount University PWS-KENT O I^7 3 PUBLISHING COMPANY E 9 U Boston CONTENTS Preface xiii Parti ORDINARY
More informationGAME PHYSICS SECOND EDITION. дяййтаййг 1 *
GAME PHYSICS SECOND EDITION DAVID H. EBERLY дяййтаййг 1 * К AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO MORGAN ELSEVIER Morgan Kaufmann Publishers
More informationAPPLIED PARTIAL DIFFERENTIAL EQUATIONS
APPLIED PARTIAL DIFFERENTIAL EQUATIONS AN I N T R O D U C T I O N ALAN JEFFREY University of Newcastle-upon-Tyne ACADEMIC PRESS An imprint of Elsevier Science Amsterdam Boston London New York Oxford Paris
More informationFinal Year M.Sc., Degree Examinations
QP CODE 569 Page No Final Year MSc, Degree Examinations September / October 5 (Directorate of Distance Education) MATHEMATICS Paper PM 5: DPB 5: COMPLEX ANALYSIS Time: 3hrs] [Max Marks: 7/8 Instructions
More informationChapter 5 HIGH ACCURACY CUBIC SPLINE APPROXIMATION FOR TWO DIMENSIONAL QUASI-LINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS
Chapter 5 HIGH ACCURACY CUBIC SPLINE APPROXIMATION FOR TWO DIMENSIONAL QUASI-LINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS 5.1 Introduction When a physical system depends on more than one variable a general
More informationTyn Myint-U Lokenath Debnath. Linear Partial Differential Equations for Scientists and Engineers. Fourth Edition. Birkhauser Boston Basel Berlin
Tyn Myint-U Lokenath Debnath Linear Partial Differential Equations for Scientists and Engineers Fourth Edition Birkhauser Boston Basel Berlin Preface to the Fourth Edition Preface to the Third Edition
More informationAn Introduction to Numerical Analysis
An Introduction to Numerical Analysis Endre Süli and David F. Mayers University of Oxford published by the press syndicate of the university of cambridge The Pitt Building, Trumpington Street, Cambridge,
More informationPreface to Second Edition... vii. Preface to First Edition...
Contents Preface to Second Edition..................................... vii Preface to First Edition....................................... ix Part I Linear Algebra 1 Basic Vector/Matrix Structure and
More informationMathematics for Chemists
Mathematics for Chemists MATHEMATICS FOR CHEMISTS D. M. Hirst Department of Molecular Sciences, university of Warwick, Coventry M D. M. Hirst 1976 All rights reserved. No part of this publication may be
More informationSyllabus (Session )
Syllabus (Session 2016-17) Department of Mathematics nstitute of Applied Sciences & Humanities AHM-1101: ENGNEERNG MATHEMATCS Course Objective: To make the students understand the concepts of Calculus,
More information9.6 Predictor-Corrector Methods
SEC. 9.6 PREDICTOR-CORRECTOR METHODS 505 Adams-Bashforth-Moulton Method 9.6 Predictor-Corrector Methods The methods of Euler, Heun, Taylor, and Runge-Kutta are called single-step methods because they use
More informationNumerical Marine Hydrodynamics Summary
Numerical Marine Hydrodynamics Summary Fundamentals of Digital Computing Error Analysis Roots of Non-linear Equations Systems of Linear Equations Gaussian Elimination Iterative Methods Optimization, Curve
More informationPartial Differential Equations
Partial Differential Equations Introduction Deng Li Discretization Methods Chunfang Chen, Danny Thorne, Adam Zornes CS521 Feb.,7, 2006 What do You Stand For? A PDE is a Partial Differential Equation This
More informationECE257 Numerical Methods and Scientific Computing. Ordinary Differential Equations
ECE257 Numerical Methods and Scientific Computing Ordinary Differential Equations Today s s class: Stiffness Multistep Methods Stiff Equations Stiffness occurs in a problem where two or more independent
More informationAN INTRODUCTION TO NUMERICAL METHODS USING MATHCAD. Mathcad Release 14. Khyruddin Akbar Ansari, Ph.D., P.E.
AN INTRODUCTION TO NUMERICAL METHODS USING MATHCAD Mathcad Release 14 Khyruddin Akbar Ansari, Ph.D., P.E. Professor of Mechanical Engineering School of Engineering and Applied Science Gonzaga University
More informationWILEY. Differential Equations with MATLAB (Third Edition) Brian R. Hunt Ronald L. Lipsman John E. Osborn Jonathan M. Rosenberg
Differential Equations with MATLAB (Third Edition) Updated for MATLAB 2011b (7.13), Simulink 7.8, and Symbolic Math Toolbox 5.7 Brian R. Hunt Ronald L. Lipsman John E. Osborn Jonathan M. Rosenberg All
More informationPage No.1. MTH603-Numerical Analysis_ Muhammad Ishfaq
Page No.1 File Version v1.5.3 Update: (Dated: 3-May-011) This version of file contains: Content of the Course (Done) FAQ updated version.(these must be read once because some very basic definition and
More informationMA1023-Methods of Mathematics-15S2 Tutorial 1
Tutorial 1 the week starting from 19/09/2016. Q1. Consider the function = 1. Write down the nth degree Taylor Polynomial near > 0. 2. Show that the remainder satisfies, < if > > 0 if > > 0 3. Show that
More informationDepartment of Mathematics California State University, Los Angeles Master s Degree Comprehensive Examination in. NUMERICAL ANALYSIS Spring 2015
Department of Mathematics California State University, Los Angeles Master s Degree Comprehensive Examination in NUMERICAL ANALYSIS Spring 2015 Instructions: Do exactly two problems from Part A AND two
More informationINSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad
Course Title Course Code INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad - 500 043 CIVIL ENGINEERING COURSE DESCRIPTION MATHEMATICS-II A30006 Course Structure Lectures Tutorials
More informationx n+1 = x n f(x n) f (x n ), n 0.
1. Nonlinear Equations Given scalar equation, f(x) = 0, (a) Describe I) Newtons Method, II) Secant Method for approximating the solution. (b) State sufficient conditions for Newton and Secant to converge.
More informationApplied Linear Algebra
Applied Linear Algebra Peter J. Olver School of Mathematics University of Minnesota Minneapolis, MN 55455 olver@math.umn.edu http://www.math.umn.edu/ olver Chehrzad Shakiban Department of Mathematics University
More information