3 (p1): PartI Linear Integral Equations 3 (p2): 1 Preliminaries 4 (p3): 1.1 Taylor Series 7 (p4): 1.2 Ordinary Differential Equations 7 (p5): 1.2.1 First Order Linear Differential Equations 9 (p6): 1.2.2 Second Order Linear Differential Equations 13 (p7): 1.2.3 The Series Solution Method 17 (p8): 1.3 Leibnitz Rule for Differentiation of Integrals 19 (p9): 1.4 Reducing Multiple Integrals to Single Integrals 22 (p10): 1.5 Laplace Transform 23 (p11): 1.5.1 Properties of Laplace Transforms 28 (p12): 1.6 Infinite Geometric Series 30 (p13): References 33 (p14): 2 Introductory Concepts of Integral Equations 34 (p15): 2.1 Classification of Integral Equations 34 (p16): 2.1.1 Fredholm Integral Equations 35 (p17): 2.1.2 Volterra Integral Equations 35 (p18): 2.1.3 Volterra-Fredholm Integral Equations 36 (p19): 2.1.4 Singular Integral Equations 37 (p20): 2.2 Classification of Integro-Differential Equations 38 (p21): 2.2.1 Fredholm Integro-Differential Equations 38 (p22): 2.2.2 Volterra Integro-Differential Equations 39 (p23): 2.2.3 Volterra-Fredholm Integro-Differential Equations 40 (p24): 2.3 Linearity and Homogeneity 40 (p25): 2.3.1 Linearity Concept 41 (p26): 2.3.2 Homogeneity Concept 42 (p27): 2.4 Origins of Integral Equations 42 (p28): 2.5 Converting IVP to Volterra Integral Equation 47 (p29): 2.5.1 Converting Volterra Integral Equation to IVP 49 (p30): 2.6 Converting BVP to Fredholm Integral Equation 54 (p31): 2.6.1 Converting Fredholm Integral Equation to BVP 59 (p32): 2.7 Solution of an Integral Equation 63 (p33): References 65 (p34): 3 Volterra Integral Equations 65 (p35): 3.1 Introduction 66 (p36): 3.2 Volterra Integral Equations of the Second Kind 66 (p37): 3.2.1 The Adomian Decomposition Method 73 (p38): 3.2.2 The Modified Decomposition Method 78 (p39): 3.2.3 The Noise Terms Phenomenon 82 (p40): 3.2.4 The...

duxiu/initial_release/线性与非线性积分方程：方法及应用：英文_12866729.zip

zlibzh/no-category/（美）佤斯瓦茨著, Abdul-Majid Wazwaz[著, 佤斯瓦茨, Wa Si Wa Ci/线性与非线性积分方程，方法及应用 英文_37438872.pdf

Linear and Nonlinear Equations Methods and Applications (Chinese Edition)

Linear and Nonlinear Integral Equations : Methods and Applications

by Abdul-Majid Wazwaz

Wazwaz, Abdul-Majid

Higher Education Press, Beijing and Springer-Verlag GmbH Berlin Heidelberg

Spektrum Akademischer Verlag. in Springer-Verlag GmbH

Steinkopff. in Springer-Verlag GmbH

Springer Verlag

Mathematics, Beijing Berlin Heidelberg, 2011

Berlin, Heidelberg, Germany, 2011

China, People's Republic, China

Springer Nature, Beijing, 2011

1st, First Edition, PS, 2011

Germany, Germany

Bei jing, 2011

Bookmarks: p1 (p3): PartⅠ Linear Integral Equations
p2 (p3): 1 Preliminaries
p3 (p4): 1.1 Taylor Series
p4 (p7): 1.2 Ordinary Differential Equations
p5 (p7): 1.2.1 First Order Linear Differential Equations
p6 (p9): 1.2.2 Second Order Linear Differential Equations
p7 (p13): 1.2.3 The Series Solution Method
p8 (p17): 1.3 Leibnitz Rule for Differentiation of Integrals
p9 (p19): 1.4 Reducing Multiple Integrals to Single Integrals
p10 (p22): 1.5 Laplace Transform
p11 (p23): 1.5.1 Properties of Laplace Transforms
p12 (p28): 1.6 Infinite Geometric Series
p13 (p30): References
p14 (p33): 2 Introductory Concepts of Integral Equations
p15 (p34): 2.1 Classification of Integral Equations
p16 (p34): 2.1.1 Fredholm Integral Equations
p17 (p35): 2.1.2 Volterra Integral Equations
p18 (p35): 2.1.3 Volterra-Fredholm Integral Equations
p19 (p36): 2.1.4 Singular Integral Equations
p20 (p37): 2.2 Classification of Integro-Differential Equations
p21 (p38): 2.2.1 Fredholm Integro-Differential Equations
p22 (p38): 2.2.2 Volterra Integro-Differential Equations
p23 (p39): 2.2.3 Volterra-Fredholm Integro-Differential Equations
p24 (p40): 2.3 Linearity and Homogeneity
p25 (p40): 2.3.1 Linearity Concept
p26 (p41): 2.3.2 Homogeneity Concept
p27 (p42): 2.4 Origins of Integral Equations
p28 (p42): 2.5 Converting IVP to Volterra Integral Equation
p29 (p47): 2.5.1 Converting Volterra Integral Equation to IVP
p30 (p49): 2.6 Converting BVP to Fredholm Integral Equation
p31 (p54): 2.6.1 Converting Fredholm Integral Equation to BVP
p32 (p59): 2.7 Solution of an Integral Equation
p33 (p63): References
p34 (p65): 3 Volterra Integral Equations
p35 (p65): 3.1 Introduction
p36 (p66): 3.2 Volterra Integral Equations of the Second Kind
p37 (p66): 3.2.1 The Adomian Decomposition Method
p38 (p73): 3.2.2 The Modified Decomposition Method
p39 (p78): 3.2.3 The Noise Terms Phenomenon
p40 (p82): 3.2.4 The Variational Iteration Method
p41 (p95): 3.2.5 The Successive Approximations Method
p42 (p99): 3.2.6 The Laplace Transform Method
p43 (p103): 3.2.7 The Series Solution Method
p44 (p108): 3.3 Volterra Integral Equations of the First Kind
p45 (p108): 3.3.1 The Series Solution Method
p46 (p111): 3.3.2 The Laplace Transform Method
p47 (p114): 3.3.3 Conversion to a Volterra Equation of the Second Kind
p48 (p118): References
p49 (p119): 4 Fredholm Integral Equations
p50 (p119): 4.1 Introduction
p51 (p121): 4.2 Fredholm Integral Equations of the Second Kind
p52 (p121): 4.2.1 The Adomian Decomposition Method
p53 (p128): 4.2.2 The Modified Decomposition Method
p54 (p133): 4.2.3 The Noise Terms Phenomenon
p55 (p136): 4.2.4 The Variational Iteration Method
p56 (p141): 4.2.5 The Direct Computation Method
p57 (p146): 4.2.6 The Successive Approximations Method
p58 (p151): 4.2.7 The Series Solution Method
p59 (p154): 4.3 Homogeneous Fredholm Integral Equation
p60 (p155): 4.3.1 The Direct Computation Method
p61 (p159): 4.4 Fredholm Integral Equations of the First Kind
p62 (p161): 4.4.1 The Method of Regularization
p63 (p166): 4.4.2 The Homotopy Perturbation Method
p64 (p173): References
p65 (p175): 5 Volterra Integro-Differential Equations
p66 (p175): 5.1 Introduction
p67 (p176): 5.2 Volterra Integro-Differential Equations of the Second Kind
p68 (p176): 5.2.1 The Adomian Decomposition Method
p69 (p181): 5.2.2 The Variational Iteration Method
p70 (p186): 5.2.3 The Laplace Transform Method
p71 (p190): 5.2.4 The Series Solution Method
p72 (p195): 5.2.5 Converting Volterra Integro-Differential Equations to Initial Value Problems
p73 (p199): 5.2.6 Converting Volterra Integro-Differential Equation to Volterra Integral Equation
p74 (p203): 5.3 Volterra Integro-Differential Equations of the First Kind
p75 (p204): 5.3.1 Laplace Transform Method
p76 (p206): 5.3.2 The Variational Iteration Method
p77 (p211): References
p78 (p213): 6 Fredholm Integro-Differential Equations
p79 (p213): 6.1 Introduction
p80 (p214): 6.2 Fredholm Integro-Differential Equations of the Second Kind
p81 (p214): 6.2.1 The Direct Computation Method
p82 (p218): 6.2.2 The Variational Iteration Method
p83 (p223): 6.2.3 The Adomian Decomposition Method
p84 (p230): 6.2.4 The Series Solution Method
p85 (p234): References
p86 (p237): 7 Abel's Integral Equation and Singular Integral Equations
p87 (p237): 7.1 Introduction
p88 (p238): 7.2 Abel's Integral Equation
p89 (p239): 7.2.1 The Laplace Transform Method
p90 (p242): 7.3 The Generalized Abel's Integral Equation
p91 (p243): 7.3.1 The Laplace Transform Method
p92 (p245): 7.3.2 The Main Generalized Abel Equation
p93 (p247): 7.4 The Weakly Singular Volterra Equations
p94 (p248): 7.4.1 The Adomian Decomposition Method
p95 (p253): 7.4.2 The Successive Approximations Method
p96 (p257): 7.4.3 The Laplace Transform Method
p97 (p260): Reterences
p98 (p261): 8 Volterra-Fredholm Integral Equations
p99 (p261): 8.1 Introduction
p100 (p262): 8.2 The Volterra-Fredholm Integral Equations
p101 (p262): 8.2.1 The Series Solution Method
p102 (p266): 8.2.2 The Adomian Decomposition Method
p103 (p269): 8.3 The Mixed Volterra-Fredholm Integral Equations
p104 (p270): 8.3.1 The Series Solution Method
p105 (p273): 8.3.2 The Adomian Decomposition Method
p106 (p277): 8.4 The Mixed Volterra-Fredholm Integral Equations in Two Variables
p107 (p278): 8.4.1 The Modified Decomposition Method
p108 (p283): References
p109 (p285): 9 Volterra-Fredholm Integro-Differential Equations
p110 (p285): 9.1 Introduction
p111 (p285): 9.2 The Volterra-Fredholm Integro-Differential Equation
p112 (p285): 9.2.1 The Series Solution Method
p113 (p289): 9.2.2 The Variational Iteration Method
p114 (p296): 9.3 The Mixed Volterra-Fredholm Integro-Differential Equations
p115 (p296): 9.3.1 The Direct Computation Method
p116 (p300): 9.3.2 The Series Solution Method
p117 (p303): 9.4 The Mixed Volterra-Fredholm Integro-Differential Equations in Two Variables
p118 (p304): 9.4.1 The Modified Decomposition Method
p119 (p309): References
p120 (p311): 10 Systems of Volterra Integral Equations
p121 (p311): 10.1 Introduction
p122 (p312): 10.2 Systems of Volterra Integral Equations of the Second Kind
p123 (p312): 10.2.1 The Adomian Decomposition Method
p124 (p318): 10.2.2 The Laplace Transform Method
p125 (p323): 10.3 Systems of Volterra Integral Equations of the First Kind
p126 (p323): 10.3.1 The Laplace Transform Method
p127 (p327): 10.3.2 Conversion to a Volterra System of the Second Kind
p128 (p328): 10.4 Systems of Volterra Integro-Differential Equations
p129 (p329): 10.4.1 The Variational Iteration Method
p130 (p335): 10.4.2 The Laplace Transform Method
p131 (p339): References
p132 (p341): 11 Systems of Fredholm Integral Equations
p133 (p341): 11.1 Introduction
p134 (p342): 11.2 Systems of Fredholm Integral Equations
p135 (p342): 11.2.1 The Adomian Decomposition Method
p136 (p347): 11.2.2 The Direct Computation Method
p137 (p352): 11.3 Systems of Fredholm Integro-Differential Equations
p138 (p353): 11.3.1 The Direct Computation Method
p139 (p358): 11.3.2 The Variational Iteration Method
p140 (p364): References
p141 (p365): 12 Systems of Singular Integral Equations
p142 (p365): 12.1 Introduction
p143 (p366): 12.2 Systems of Generalized Abel Integral Equations
p144 (p366): 12.2.1 Systems of Generalized Abel Integral Equations in Two Unknowns
p145 (p370): 12.2.2 Systems of Generalized Abel Integral Equations in Three Unknowns
p146 (p374): 12.3 Systems of the Weakly Singular Volterra Integral Equations
p147 (p374): 12.3.1 The Laplace Transform Method
p148 (p378): 12.3.2 The Adomian Decomposition Method
p149 (p383): References
p150 (p387): PartII Nonlinear Integral Equations
p151 (p387): 13 Nonlinear Volterra Integral Equations
p152 (p387): 13.1 Introduction
p153 (p388): 13.2 Existence of the Solution for Nonlinear Volterra Integral Equations
p154 (p388): 13.3 Nonlinear Volterra Integral Equations of the Second Kind
p155 (p389): 13.3.1 The Successive Approximations Method
p156 (p393): 13.3.2 The Series Solution Method
p157 (p397): 13.3.3 The Adomian Decomposition Method
p158 (p404): 13.4 Nonlinear Volterra Integral Equations of the First Kind
p159 (p405): 13.4.1 The Laplace Transform Method
p160 (p408): 13.4.2 Conversion to a Volterra Equation of the Second Kind
p161 (p411): 13.5 Systems of Nonlinear Volterra Integral Equations
p162 (p412): 13.5.1 Systems of Nonlinear Volterra Integral Equations of the Second Kind
p163 (p417): 13.5.2 Systems of Nonlinear Volterra Integral Equations of the First Kind
p164 (p423): References
p165 (p425): 14 Nonlinear Volterra Integro-Differential Equations
p166 (p425): 14.1 Introduction
p167 (p426): 14.2 Nonlinear Volterra Integro-Differential Equations of the Second Kind
p168 (p426): 14.2.1 The Combined Laplace Transform-Adomian Decomposition Method
p169 (p432): 14.2.2 The Variational Iteration Method
p170 (p436): 14.2.3 The Series Solution Method
p171 (p440): 14.3 Nonlinear Volterra Integro-Differential Equations of the First Kind
p172 (p440): 14.3.1 The Combined Laplace Transform-Adomian Decomposition Method
p173 (p446): 14.3.2 Conversion to Nonlinear Volterra Equation of the Second Kind
p174 (p450): 14.4 Systems of Nonlinear Volterra Integro-Differential Equations
p175 (p451): 14.4.1 The Variational Iteration Method
p176 (p456): 14.4.2 The Combined Laplace Transform-Adomian Decomposition Method
p177 (p465): References
p178 (p467): 15 Nonlinear Fredholm Integral Equations
p179 (p467): 15.1 Introduction
p180 (p468): 15.2 Existence of the Solution for Nonlinear Fredholm Integral Equations
p181 (p469): 15.2.1 Bifurcation Points and Singular Points
p182 (p469): 15.3 Nonlinear Fredholm Integral Equations of the Second Kind
p183 (p470): 15.3.1 The Direct Computation Method
p184 (p476): 15.3.2 The Series Solution Method
p185 (p480): 15.3.3 The Adomian Decomposition Method
p186 (p485): 15.3.4 The Successive Approximations Method
p187 (p490): 15.4 Homogeneous Nonlinear Fredholm Integral Equations
p188 (p490): 15.4.1 The Direct Computation Method
p189 (p494): 15.5 Nonlinear Fredholm Integral Equations of the First Kind
p190 (p495): 15.5.1 The Method of Regularization
p191 (p500): 15.5.2 The Homotopy Perturbation Method
p192 (p505): 15.6 Systems of Nonlinear Fredholm Integral Equations
p193 (p506): 15.6.1 The Direct Computation Method
p194 (p510): 15.6.2 The Modified Adomian Decomposition Method
p195 (p515): References
p196 (p517): 16 Nonlinear Fredholm Integro-Differential Equations
p197 (p517): 16.1 Introduction
p198 (p518): 16.2 Nonlinear Fredholm Integro-Differential Equations
p199 (p518): 16.2.1 The Direct Computation Method
p200 (p522): 16.2.2 The Variational Iteration Method
p201 (p526): 16.2.3 The Series Solution Method
p202 (p530): 16.3 Homogeneous Nonlinear Fredholm Integro-Differential Equations
p203 (p530): 16.3.1 The Direct Computation Method
p204 (p535): 16.4 Systems of Nonlinear Fredholm Integro-Differential Equations
p205 (p535): 16.4.1 The Direct Computation Method
p206 (p540): 16.4.2 The Variational Iteration Method
p207 (p545): References
p208 (p547): 17 Nonlinear Singular Integral Equations
p209 (p547): 17.1 Introduction
p210 (p548): 17.2 Nonlinear Abel's Integral Equation
p211 (p549): 17.2.1 The Laplace Transform Method
p212 (p552): 17.3 The Generalized Nonlinear Abel Equation
p213 (p553): 17.3.1 The Laplace Transform Method
p214 (p556): 17.3.2 The Main Generalized Nonlinear Abel Equation
p215 (p559): 17.4 The Nonlinear Weakly-Singular Volterra Equations
p216 (p559): 17.4.1 The Adomian Decomposition Method
p217 (p562): 17.5 Systems of Nonlinear Weakly-Singular Volterra Integral Equations
p218 (p563): 17.5.1 The Modified Adomian Decomposition Method
p219 (p567): References
p220 (p569): 18 Applications of Integral Equations
p221 (p569): 18.1 Introduction
p222 (p570): 18.2 Volterra's Population Model
p223 (p571): 18.2.1 The Variational Iteration Method
p224 (p572): 18.2.2 The Series Solution Method
p225 (p573): 18.2.3 The PadéApproximants
p226 (p574): 18.3 Integral Equations with Logarithmic Kernels
p227 (p577): 18.3.1 Second Kind Fredholm Integral Equation with a Logarithmic Kernel
p228 (p580): 18.3.2 First Kind Fredholm Integral Equation with a Logarithmic Kernel
p229 (p583): 18.3.3 Another First Kind Fredholm Integral Equation with a Logarithmic Kernel
p230 (p584): 18.4 The Fresnel Integrals
p231 (p587): 18.5 The Thomas-Fermi Equation
p232 (p590): 18.6 Heat Transfer and Heat Radiation
p233 (p590): 18.6.1 Heat Transfer:Lighthill Singular Integral Equation
p234 (p592): 18.6.2 Heat Radiation in a Semi-Infinite Solid
p235 (p594): References
p236 (p597): Appendix A Table of Indefinite Integrals
p237 (p597): A.1 Basic Forms
p238 (p597): A.2 Trigonometric Forms
p239 (p598): A.3 Inverse Trigonometric Forms
p240 (p598): A.4 Exponential and Logarithmic Forms
p241 (p599): A.5 Hyperbolic Forms
p242 (p599): A.6 Other Forms
p243 (p600): Appendix B Integrals Involving Irrational Algebraic Functions
p244 (p600): B.1 Integrals Involving？,n is an integer,n≥0
p245 (p600): B.2 Integrals Involving？,n is an odd integer,n≥1
p246 (p601): Appendix C Series Representations
p247 (p601): C.1 Exponential Functions Series
p248 (p601): C.2 Trigonometric Functions
p249 (p602): C.3 Inverse Trigonometric Functions
p250 (p602): C.4 Hyperbolic Functions
p251 (p602): C.5 Inverse Hyperbolic Functions
p252 (p602): C.6 Logarithmic Functions
p253 (p603): Appendix D The Error and the Complementary Error Functions
p254 (p603): D.1 The Error Function
p255 (p603): D.2 The Complementary Error Function
p256 (p604): Appendix E Gamma Function
p257 (p605): Appendix F Infinite Series
p258 (p605): F.1 Numerical Series
p259 (p605): F.2 Trigonometric Series
p260 (p607): Appendix G The Fresnel Integrals
p261 (p607): G.1 The Fresnel Cosine Integral
p262 (p607): G.2 The Fresnel Sine Integral
p263 (p609): Answers
p264 (p637): Index

related_files:
filepath:12866729_《线性与非线性积分方程:方法及应用:英文》.zip — md5:9dc4bb3fce68c87f7c34e34ac7235a1d — filesize:31893644
filepath:线性与非线性积分方程:方法及应用:英文_12866729.zip — md5:7f7570949413534692bf99e03cf486e5 — filesize:33248492
filepath:线性与非线性积分方程:方法及应用:英文_12866729.zip — md5:ec0d79584cfdefb75870da5821e7a6e9 — filesize:33248492
filepath:12866729.rar — md5:cbdc0267f67dbbdc7ef38a3acb902f1a — filesize:31924236
filepath:12866729.zip — md5:95301621fmdebd7b3dd7c3821b14540f — filesize:33248492
filepath:/读秀/读秀4.0/读秀/4.0/数据库19-2/线性与非线性积分方程:方法及应用:英文_12866729.zip
filepath:/读秀/读秀3.0/读秀/3.0/3.0新/其余书库等多个文件/0110/68/12866729.zip
filepath:第八部分/NNNNNNN/68/12866729.zip

MiU

Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear integral equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Padé approximants. ¡ This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering. It can also be used as a text for advanced undergraduate and ¡graduate students in applied mathematics, science and engineering, and related fields. ¡ Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA. ¡ ¡

Linear and Nonlinear Integral Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear integral equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Pade approximants.
This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering. It can also be used as a text for advanced undergraduate and graduate students in applied mathematics, science and engineering, and related fields.
Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA.
"

2024-06-13