本书的目的是为解决由科学，工程和数学金融领域的随机微分方程模型提出的问题提供有益的理解。 通常，这些问题需要使用数值方法来获得解决方案。
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Differential Equations and Linear Algebra(4th) 英文无水印原版pdf 第4版 pdf所有页面使用FoxitReader、PDF-XChangeViewer、SumatraPDF和Firefox测试都可以打开 本资源转载自网络，如有侵权，请联系上传者或csdn删除查看此书详细信息请在美国亚马逊官网搜索此书
Editorial Director, Mathematics: Christine hoagEditor-in-Chief: Deirdre LynchAcquisitions Editor: William HoffmaProject Team Lead: Christina leProject manager: Lauren MorseEditorial Assistant: Jennifer SnyderProgram Team Lead: Karen wernholmProgram Manager Danielle simbajonCover and illustration Design: Studio MontageProgram Design Lead: Beth PaquinProduct Marketing Manager Claire KozarProduct Marketing Coordiator: Brooke smithField Marketing Manager: Evan St CyrSenior Author Support/Technology Specialist: Joe vetereSenior Procurement Specialist: Carol MelvilleInterior Design, Production Management, Answer Art, and CompositioneNergizer Aptara, LtdCover Image: Light trails on modern building background in Shanghai, China-hxdyl/123RFCopyright O2017, 2011, 2005 Pearson Education, Inc. or its affiliates. All Rights Reserved. Printed in the United States ofAmerica. This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibitedreproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopyingrecording, or otherwise. For information regarding permissions, request forms and the appropriate contacts within the PearsonEducationGlobalRights&Permissionsdepartmentpleasevisitwww.pearsoned.com/permissions/PEARSON and ALWAYS LEARNING are exclusive trademarks in the U.s. and/or other countries owned by Pearson Education, Inc.or its affiliatesUnless otherwise indicated herein, any third-party trademarks that may appear in this work are the property of their respective owand any references to third-party trademarks, logos or other trade dress are for demonstrative or descriptive purposes only. Suchof such marks or any relationship between the owner and Pearson Education, Inc. or its affiliates, authors, licensees or distributor treferences are not intended to imply any sponsorship, endorsement, authorization, or promotion of Pearsons products by the ownersLibrary of Congress Cataloging-in-Publication DataGoode. Stephen wDifferential equations and linear algebra/Stephen W. Goode and Scott A. AnninCalifornia state University, Fullerton. -4th editionpages cmIncludes indexISBN978-0-321-96467-0—ISBN0-32196467-51. Differential equations. 2. Algebras, Linear. I. Annin, Scott. II. TitleQA371.G6442015515’.35-dc23201400601512345678910V031-1918171615PEARSONISBN10:0-321-96467-5www.pearsonhighered.comISBN13:978-0-321-96467-0ContentsPreface vii1 First-Order Differential Equations1.1 Differential Equations Everywhere 11.2 Basic Ideas and Terminology 131.3 The Geometry of First-Order Differential Equations 231.4 Separable Differential Equations 341.5 Some Simple Population Models 451.6 First-Order Linear Differential Equations 531.7 Modeling Problems Using First-Order LinearDifferential Equations 61.8 Change of variables 711.9 Exact Differential Equations 821.10 Numerical solution to first-Order DifferentialEquations 931.11 Some Higher-Order Differential Equations 1011.12 Chapter Review 1062 Matrices and Systems of LinearEquations1142.1 Matrices: Definitions and notation 1152.2 Matrix Algebra 1222.3 Terminology for Systems of Linear Equations 13824R。 w-Echelon Matrices and Elementary R。wOperations 1462.5 Gaussian elimination 1562.6 The Inverse of a square matrix 1682.7 Elementary Matrices and the LU Factorization 1792. 8 The Invertible matrix theorem i 1882.9 Chapter Review 1903 Determinants1963.1 The Definition of the determinant 1963.2 Properties of Determinants 2093.3 Cofactor Expansions 2223. 4 Summary of Determinants 2353.5 Chapter Review 242iy Contents4 Vector Spaces2464.1 Vectors in rn 2484.2 Definition of a Vector Space 2524.3 Subspaces 2634.4 Spanning Sets 2744.5 Linear Dependence and Linear Independence 2844.6 Bases and dimension 2984.7 Change of basis 31 14.8 Row Space and Column Space 3194. 9 The Rank-Nullity Theorem 3254.10 Invertible Matrix Theorem ll 3314.11 Chapter Review 3325 Inner Product Spaces3395.1 Definition of an Inner product space 3405.2 Orthogonal Sets of vectors and orthogonalProjections 3525.3 The gram -Schmidt process 3625.4 Least Squares Approximation 3665.5 Chapter Review 3766 Linear Transformations3796.1 Definition of a linear transformation 3806.2 Transformations of r2 3916.3 The Kernel and range of a linear transformation 3976. 4 Additional Properties of Linear Transformations 4076.5 The matrix of a linear transformation 4196.6 Chaiter review 4287 Eigenvalues and Eigenvectors4337.1 The Eigenvalue/Eigenvector Problem 4347.2 General Results for Eigenvalues and Eigenvectors 4467. 3 Diagonalization 4547.4 An Introduction to the Matrix Exponential Function 4627.5 Orthogonal Diagonalization and Quadratic forms 4667.6 Jordan canonical forms 4757.7 Chapter review 4888 Linear Differential Equations ofOrder n4938.1 General Theory for Linear Differential Equations 4958.2 Constant Coefficient Homogeneous LinearDifferential Equations 5058.3 The method of undetermined coefficientsAnnihilators 5158.4 Complex-Valued Trial Solutions 5268.5 Oscillations of a Mechanical System 529Contents v8.6 RLC Circuits 5428.7 The Variation of parameters method 5478. 8 A Differential Equation with Nonconstant Coefficients 5578.9 Reduction of order 5688.10 Chapter Review 5739 Systems of Differential Equations5809.1 First-Order Linear Systems 5829.2 Vector Formulation 5889.3 General Results for first-Order Linear Differentialystems 5939.4 Vector Differential Equations: NondefectiveCoefficient Matrix 5999.5 Vector Differential Equations: Defective CoefficientMatrix 6089.6 Variation-of-Parameters for Linear Systems 6209.7 Some Applications of Linear Systems of DifferentialEquations 6259.8 Matrix Exponential Function and Systems ofDifferential Equations 6359.9 The Phase Plane for Linear Autonomous Systems 6439.10 Nonlinear Systems 6559.11 Chapter Review 66310 The Laplace Transform and SomeElementary Applications67010.1 Definition of the Laplace Transform 67010.2 The Existence of the laplace transform and theInverse transform 67610.3 Periodic Functions and the Laplace transform 68210. 4 The transform of derivatives and solution ofInitial-Value problems 68510.5 The First Shifting Theorem 69010.6 The Unit Step Function 69510.7 The Second Shifting Theorem 69910.8 Impulsive Driving Terms: The Dirac Delta Function 70610.9 The Convolution Integral 71110.10 Chapter Review 71711 Series Solutions to Linear DifferentiaEquations72211.1 A Review of power series 72311.2 Series Solutions about an Ordinary Point 73111.3 The Legendre Equation 74111.4 Series Solutions about a Regular Singular Point 75011.5 Frobenius theory 75911.6 Bessel's Equation of Order p 77311.7 Chapter review 785Vi ContentsA Review of Complex Numbers791B Review of Partial Fractions797C Review of Integration Techniques804D Linearly Independent Solutions tox2y+xp(x)y+g(x)y=0811Answers to odd-NumberedExercises814Index 849S.W. Goode dedicates this book to megan and tobiS. A. annin dedicates this book to arthur and Juliann the bestparents anyone could ask forPretraceLike the first three editions of Differential Equations and Linear algebra, this fourthedition is intended for a sophomore level course that covers material in both differentialequations and linear algebra. In writing this text we have endeavored to develop the students appreciation for the power of the general vector space framework in formulatingand solving linear problems. The material is accessible to science and engineering stu-dents who have completed three semesters of calculus and who bring the maturity of thatsuccess with them to this course This text is written as we would naturally teach blending an abundance of examples and illustrations, but not at the expense of a deliberateand rigorous treatment. Most results are proven in detail However, many of these can beskipped in favor of a more problem-solving oriented approach depending on the reader'sobjectives. Some readers may like to incorporate some form of technology(computeralgebra system(CAS)or graphing calculator) and there are several instances in the textwhere the power of technology is illustrated using the Cas Maple. Furthermore, manyexercise sets have problems that require some form of technology for their solutionThese problems are designated with a oIn developing the fourth edition we have once more kept maximum flexibility ofthe material in mind. In so doing, the text can effectively accommodate the differentemphases that can be placed in a combined differential equations and linear algebracourse, the varying backgrounds of students who enroll in this type of course, and thefact that different institutions have different credit values for such a course. The wholetext can be covered in a five credit-hour course. For courses with a lower credit-hourvalue, some selectivity will have to be exercised. For example, much(or all) of ChapterI may be omitted since most students will have seen many of these differential equationstopics in an earlier calculus course, and the remainder of the text does not depend onthe techniques introduced in this chapter. Alternatively, while one of the major goalsof the text is to interweave the material on differential equations with the tools fromlinear algebra in a symbiotic relationship as much as possible, the core material on linearalgebra is given in Chapters 2-7 so that it is possible to use this book for a course thatfocuses solely on the linear algebra presented in these six chapters. The material ondifferential equations is contained primarily in Chapters 1 and 8-1l, and readers whohave already taken a first course in linear algebra can choose to proceed directly to thesechaptersThere are other means of eliminating sections to reduce the amount of material tobe covered in a course. Section 2. 7 contains material that is not required elsewhere inthe text, Chapter 3 can be condensed to a single section(Section 3. 4) for readers needingonly a cursory overview of determinants, and Sections 4.7, 5.4, and the later sections ofChapters 6 and 7 could all be reserved for a second course in linear algebra. In Chapter 8Sections 8.4, 8.8, and 8.9 can be omitted, and, depending on the goals of the course, Sections 8.5 and 8.6 could either be de-emphasized or omitted completely Similar remarksapply to Sections 9.7-9.10. At California State University, Fullerton we have a fourcredit-hour course for sophomores that is based around the material in Chapters 1-9viii PrefaceMajor Changes in the Fourth EditionSeveral sections of the text have been modified to improve the clarity of the presentationand to provide new examples that reflect insightful illustrations we have used in our owncourses at California State University, Fullerton. Other significant changes within thetext are listed beleOW1. The chapter on vector spaces in the previous edition has been split into two chaptersChapters 4 and 5) in the present edition, in order to focus separate attention onvector spaces and inner product spaces. The shorter length of these two chaptersis also intended to make each of them less daunting2. The chapter on inner product spaces( Chapter 5)includes a new section providingan application of linear algebra to the subject of least squares approximation3. The chapter on linear transformations in the previous edition has been split intotwo chapters( Chapters 6 and 7)in the present edition. Chapter 6 is focused onlinear transformations, while Chapter 7 places direct emphasis on the theory ofeigenvalues and eigenvectors. Once more, readers should find the shorter chapterscovering these topics more approachable and focused4. Most exercise sets have been enlarged or rearranged. Over 3, 000 problems are nowcontained within the text, and more than 600 concept -oriented true/false items arealso included in the text5. Every chapter of the book includes one or more optional projects that allow formore in-depth study and application of the topics found in the text6. The back of the book now includes the answer to every True-False review itemcontained in the textAcknowledgmentsWe would like to acknowledge the thoughtful input from the following reviewers ofthe fourth edition: Jamey Bass of City College of San Francisco, Tamar Friedmann ofUniversity of rochester, and linghai Zhang of Lehigh UniversityAll of their comments were considered carefully in the preparation of the textS.A. Annin: I once more thank my parents, Arthur and Juliann Annin, for their loveand encouragement in all of my professional endeavors. I also gratefully acknowledgethe many students who have taken this course with me over the years and, in so doinghave enhanced my love for these topics and deeply enriched my career as a professorFirst-Order DifferentiaEquations1.1 Differential Equations Everywherea differential equation is any equation that involves one or more derivatives of anunknown function. For example(1.1.1dxds(S-1)(1.1.2)are differential equations. In the differential equation(1. 1.1) the unknown function ordependent variable is y, and x is the independent variable; in the differential equation(1. 1.2)the dependent and independent variables are S and t, respectively. Differentialequations such as(1.1.1)and(1.1.)in which the unknown function depends only ona single independent variable are called ordinary differential equations. By contrast,the differential equation Laplace's equation)0involves partial derivatives of the unknown functionu(x, y)of two independent variablesx and y. Such differential equations are called partial differential equationsOne way in which differential equations can be characterized is by the order of thehighest derivative that occurs in the differential equation This number is called the orderof the differential equation. Thus, (l 1.1) has order two, whereas (1. 1. 2)is a first-orderdifferential equation1
Editorial Director, Mathematics: Christine hoagEditor-in-Chief: Deirdre LynchAcquisitions Editor: William HoffmaProject Team Lead: Christina leProject manager: Lauren MorseEditorial Assistant: Jennifer SnyderProgram Team Lead: Karen wernholmProgram Manager Danielle simbajonCover and illustration Design: Studio MontageProgram Design Lead: Beth PaquinProduct Marketing Manager Claire KozarProduct Marketing Coordiator: Brooke smithField Marketing Manager: Evan St CyrSenior Author Support/Technology Specialist: Joe vetereSenior Procurement Specialist: Carol MelvilleInterior Design, Production Management, Answer Art, and CompositioneNergizer Aptara, LtdCover Image: Light trails on modern building background in Shanghai, China-hxdyl/123RFCopyright O2017, 2011, 2005 Pearson Education, Inc. or its affiliates. All Rights Reserved. Printed in the United States ofAmerica. This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibitedreproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopyingrecording, or otherwise. For information regarding permissions, request forms and the appropriate contacts within the PearsonEducationGlobalRights&Permissionsdepartmentpleasevisitwww.pearsoned.com/permissions/PEARSON and ALWAYS LEARNING are exclusive trademarks in the U.s. and/or other countries owned by Pearson Education, Inc.or its affiliatesUnless otherwise indicated herein, any third-party trademarks that may appear in this work are the property of their respective owand any references to third-party trademarks, logos or other trade dress are for demonstrative or descriptive purposes only. Suchof such marks or any relationship between the owner and Pearson Education, Inc. or its affiliates, authors, licensees or distributor treferences are not intended to imply any sponsorship, endorsement, authorization, or promotion of Pearsons products by the ownersLibrary of Congress Cataloging-in-Publication DataGoode. Stephen wDifferential equations and linear algebra/Stephen W. Goode and Scott A. AnninCalifornia state University, Fullerton. -4th editionpages cmIncludes indexISBN978-0-321-96467-0—ISBN0-32196467-51. Differential equations. 2. Algebras, Linear. I. Annin, Scott. II. TitleQA371.G6442015515’.35-dc23201400601512345678910V031-1918171615PEARSONISBN10:0-321-96467-5www.pearsonhighered.comISBN13:978-0-321-96467-0ContentsPreface vii1 First-Order Differential Equations1.1 Differential Equations Everywhere 11.2 Basic Ideas and Terminology 131.3 The Geometry of First-Order Differential Equations 231.4 Separable Differential Equations 341.5 Some Simple Population Models 451.6 First-Order Linear Differential Equations 531.7 Modeling Problems Using First-Order LinearDifferential Equations 61.8 Change of variables 711.9 Exact Differential Equations 821.10 Numerical solution to first-Order DifferentialEquations 931.11 Some Higher-Order Differential Equations 1011.12 Chapter Review 1062 Matrices and Systems of LinearEquations1142.1 Matrices: Definitions and notation 1152.2 Matrix Algebra 1222.3 Terminology for Systems of Linear Equations 13824R。 w-Echelon Matrices and Elementary R。wOperations 1462.5 Gaussian elimination 1562.6 The Inverse of a square matrix 1682.7 Elementary Matrices and the LU Factorization 1792. 8 The Invertible matrix theorem i 1882.9 Chapter Review 1903 Determinants1963.1 The Definition of the determinant 1963.2 Properties of Determinants 2093.3 Cofactor Expansions 2223. 4 Summary of Determinants 2353.5 Chapter Review 242iy Contents4 Vector Spaces2464.1 Vectors in rn 2484.2 Definition of a Vector Space 2524.3 Subspaces 2634.4 Spanning Sets 2744.5 Linear Dependence and Linear Independence 2844.6 Bases and dimension 2984.7 Change of basis 31 14.8 Row Space and Column Space 3194. 9 The Rank-Nullity Theorem 3254.10 Invertible Matrix Theorem ll 3314.11 Chapter Review 3325 Inner Product Spaces3395.1 Definition of an Inner product space 3405.2 Orthogonal Sets of vectors and orthogonalProjections 3525.3 The gram -Schmidt process 3625.4 Least Squares Approximation 3665.5 Chapter Review 3766 Linear Transformations3796.1 Definition of a linear transformation 3806.2 Transformations of r2 3916.3 The Kernel and range of a linear transformation 3976. 4 Additional Properties of Linear Transformations 4076.5 The matrix of a linear transformation 4196.6 Chaiter review 4287 Eigenvalues and Eigenvectors4337.1 The Eigenvalue/Eigenvector Problem 4347.2 General Results for Eigenvalues and Eigenvectors 4467. 3 Diagonalization 4547.4 An Introduction to the Matrix Exponential Function 4627.5 Orthogonal Diagonalization and Quadratic forms 4667.6 Jordan canonical forms 4757.7 Chapter review 4888 Linear Differential Equations ofOrder n4938.1 General Theory for Linear Differential Equations 4958.2 Constant Coefficient Homogeneous LinearDifferential Equations 5058.3 The method of undetermined coefficientsAnnihilators 5158.4 Complex-Valued Trial Solutions 5268.5 Oscillations of a Mechanical System 529Contents v8.6 RLC Circuits 5428.7 The Variation of parameters method 5478. 8 A Differential Equation with Nonconstant Coefficients 5578.9 Reduction of order 5688.10 Chapter Review 5739 Systems of Differential Equations5809.1 First-Order Linear Systems 5829.2 Vector Formulation 5889.3 General Results for first-Order Linear Differentialystems 5939.4 Vector Differential Equations: NondefectiveCoefficient Matrix 5999.5 Vector Differential Equations: Defective CoefficientMatrix 6089.6 Variation-of-Parameters for Linear Systems 6209.7 Some Applications of Linear Systems of DifferentialEquations 6259.8 Matrix Exponential Function and Systems ofDifferential Equations 6359.9 The Phase Plane for Linear Autonomous Systems 6439.10 Nonlinear Systems 6559.11 Chapter Review 66310 The Laplace Transform and SomeElementary Applications67010.1 Definition of the Laplace Transform 67010.2 The Existence of the laplace transform and theInverse transform 67610.3 Periodic Functions and the Laplace transform 68210. 4 The transform of derivatives and solution ofInitial-Value problems 68510.5 The First Shifting Theorem 69010.6 The Unit Step Function 69510.7 The Second Shifting Theorem 69910.8 Impulsive Driving Terms: The Dirac Delta Function 70610.9 The Convolution Integral 71110.10 Chapter Review 71711 Series Solutions to Linear DifferentiaEquations72211.1 A Review of power series 72311.2 Series Solutions about an Ordinary Point 73111.3 The Legendre Equation 74111.4 Series Solutions about a Regular Singular Point 75011.5 Frobenius theory 75911.6 Bessel's Equation of Order p 77311.7 Chapter review 785Vi ContentsA Review of Complex Numbers791B Review of Partial Fractions797C Review of Integration Techniques804D Linearly Independent Solutions tox2y+xp(x)y+g(x)y=0811Answers to odd-NumberedExercises814Index 849S.W. Goode dedicates this book to megan and tobiS. A. annin dedicates this book to arthur and Juliann the bestparents anyone could ask forPretraceLike the first three editions of Differential Equations and Linear algebra, this fourthedition is intended for a sophomore level course that covers material in both differentialequations and linear algebra. In writing this text we have endeavored to develop the students appreciation for the power of the general vector space framework in formulatingand solving linear problems. The material is accessible to science and engineering stu-dents who have completed three semesters of calculus and who bring the maturity of thatsuccess with them to this course This text is written as we would naturally teach blending an abundance of examples and illustrations, but not at the expense of a deliberateand rigorous treatment. Most results are proven in detail However, many of these can beskipped in favor of a more problem-solving oriented approach depending on the reader'sobjectives. Some readers may like to incorporate some form of technology(computeralgebra system(CAS)or graphing calculator) and there are several instances in the textwhere the power of technology is illustrated using the Cas Maple. Furthermore, manyexercise sets have problems that require some form of technology for their solutionThese problems are designated with a oIn developing the fourth edition we have once more kept maximum flexibility ofthe material in mind. In so doing, the text can effectively accommodate the differentemphases that can be placed in a combined differential equations and linear algebracourse, the varying backgrounds of students who enroll in this type of course, and thefact that different institutions have different credit values for such a course. The wholetext can be covered in a five credit-hour course. For courses with a lower credit-hourvalue, some selectivity will have to be exercised. For example, much(or all) of ChapterI may be omitted since most students will have seen many of these differential equationstopics in an earlier calculus course, and the remainder of the text does not depend onthe techniques introduced in this chapter. Alternatively, while one of the major goalsof the text is to interweave the material on differential equations with the tools fromlinear algebra in a symbiotic relationship as much as possible, the core material on linearalgebra is given in Chapters 2-7 so that it is possible to use this book for a course thatfocuses solely on the linear algebra presented in these six chapters. The material ondifferential equations is contained primarily in Chapters 1 and 8-1l, and readers whohave already taken a first course in linear algebra can choose to proceed directly to thesechaptersThere are other means of eliminating sections to reduce the amount of material tobe covered in a course. Section 2. 7 contains material that is not required elsewhere inthe text, Chapter 3 can be condensed to a single section(Section 3. 4) for readers needingonly a cursory overview of determinants, and Sections 4.7, 5.4, and the later sections ofChapters 6 and 7 could all be reserved for a second course in linear algebra. In Chapter 8Sections 8.4, 8.8, and 8.9 can be omitted, and, depending on the goals of the course, Sections 8.5 and 8.6 could either be de-emphasized or omitted completely Similar remarksapply to Sections 9.7-9.10. At California State University, Fullerton we have a fourcredit-hour course for sophomores that is based around the material in Chapters 1-9viii PrefaceMajor Changes in the Fourth EditionSeveral sections of the text have been modified to improve the clarity of the presentationand to provide new examples that reflect insightful illustrations we have used in our owncourses at California State University, Fullerton. Other significant changes within thetext are listed beleOW1. The chapter on vector spaces in the previous edition has been split into two chaptersChapters 4 and 5) in the present edition, in order to focus separate attention onvector spaces and inner product spaces. The shorter length of these two chaptersis also intended to make each of them less daunting2. The chapter on inner product spaces( Chapter 5)includes a new section providingan application of linear algebra to the subject of least squares approximation3. The chapter on linear transformations in the previous edition has been split intotwo chapters( Chapters 6 and 7)in the present edition. Chapter 6 is focused onlinear transformations, while Chapter 7 places direct emphasis on the theory ofeigenvalues and eigenvectors. Once more, readers should find the shorter chapterscovering these topics more approachable and focused4. Most exercise sets have been enlarged or rearranged. Over 3, 000 problems are nowcontained within the text, and more than 600 concept -oriented true/false items arealso included in the text5. Every chapter of the book includes one or more optional projects that allow formore in-depth study and application of the topics found in the text6. The back of the book now includes the answer to every True-False review itemcontained in the textAcknowledgmentsWe would like to acknowledge the thoughtful input from the following reviewers ofthe fourth edition: Jamey Bass of City College of San Francisco, Tamar Friedmann ofUniversity of rochester, and linghai Zhang of Lehigh UniversityAll of their comments were considered carefully in the preparation of the textS.A. Annin: I once more thank my parents, Arthur and Juliann Annin, for their loveand encouragement in all of my professional endeavors. I also gratefully acknowledgethe many students who have taken this course with me over the years and, in so doinghave enhanced my love for these topics and deeply enriched my career as a professorFirst-Order DifferentiaEquations1.1 Differential Equations Everywherea differential equation is any equation that involves one or more derivatives of anunknown function. For example(1.1.1dxds(S-1)(1.1.2)are differential equations. In the differential equation(1. 1.1) the unknown function ordependent variable is y, and x is the independent variable; in the differential equation(1. 1.2)the dependent and independent variables are S and t, respectively. Differentialequations such as(1.1.1)and(1.1.)in which the unknown function depends only ona single independent variable are called ordinary differential equations. By contrast,the differential equation Laplace's equation)0involves partial derivatives of the unknown functionu(x, y)of two independent variablesx and y. Such differential equations are called partial differential equationsOne way in which differential equations can be characterized is by the order of thehighest derivative that occurs in the differential equation This number is called the orderof the differential equation. Thus, (l 1.1) has order two, whereas (1. 1. 2)is a first-orderdifferential equation1
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Elementary Differential Equations and Boundary Value Problems 10th edition
学习 differential equation 的一本基本的书，很多大学都以这本书为教材
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PDE Evans 现代偏微分(Partical Differential Equations)pde 答案 solutions
Evans PDE solution Evans 现代偏微分 答案
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