

Elementary Differential Equations and Boundary Value Problems, 10th Edition 


William E. Boyce



°¡°Ý : \42,000 
ISBN : 9781118323618 
ÃâÆÇ»ç : Wiley 
ÃâÆÇ³â : 2013 
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The new 10th edition of Elementary Differential Equations and Boundary Value Problems, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. The 9th edition includes new problems and examples, as well as expanded explanations to help motivate students. The book is written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for reading the book is a working knowledge of calculus, gained from a normal two or threesemester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.



Preface Chapter 1 Introduction 1 1.1 Some Basic Mathematical Models; Direction Fields 1.2 Solutions of Some Differential Equations 1.3 Classification of Differential Equations 1.4 Historical Remarks Chapter 2 First Order Differential Equations 2.1 Linear Equations; Method of Integrating Factors 2.2 Separable Equations 2.3 Modeling with First Order Equations 2.4 Differences Between Linear and Nonlinear Equations 2.5 Autonomous Equations and Population Dynamics 2.6 Exact Equations and Integrating Factors 2.7 Numerical Approximations: Euler's Method 2.8 The Existence and Uniqueness Theorem 2.9 First Order Difference Equations
Chapter 3 Second Order Linear Equations 135 3.1 Homogeneous Equations with Constant Coefficients 3.2 Fundamental Solutions of Linear Homogeneous Equations; The Wronskian 3.3 Complex Roots of the Characteristic Equation 3.4 Repeated Roots; Reduction of Order 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients 3.6 Variation of Parameters 3.7 Mechanical and Electrical Vibrations 3.8 Forced Vibrations
Chapter 4 Higher Order Linear Equations 4.1 General Theory of nth Order Linear Equations 4.2 Homogeneous Equations with Constant Coefficients 4.3 The Method of Undetermined Coefficients 4.4 The Method of Variation of Parameters
Chapter 5 Series Solutions of Second Order Linear Equations 5.1 Review of Power Series 5.2 Series Solutions Near an Ordinary Point, Part I 5.3 Series Solutions Near an Ordinary Point, Part II 5.4 Euler Equations; Regular Singular Points 5.5 Series Solutions Near a Regular Singular Point, Part I 5.6 Series Solutions Near a Regular Singular Point, Part II 5.7 Bessel's Equation
Chapter 6 The Laplace Transform 6.1 Definition of the Laplace Transform 6.2 Solution of Initial Value Problems 6.3 Step Functions 6.4 Differential Equations with Discontinuous Forcing Functions 6.5 Impulse Functions 6.6 The Convolution Integral
Chapter 7 Systems of First Order Linear Equations 7.1 Introduction 7.2 Review of Matrices 7.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors 7.4 Basic Theory of Systems of First Order Linear Equations 7.5 Homogeneous Linear Systems with Constant Coefficients? 7.6 Complex Eigenvalues 7.7 Fundamental Matrices 7.8 Repeated Eigenvalues 7.9 Nonhomogeneous Linear Systems
Chapter 8 Numerical Methods 8.1 The Euler or Tangent Line Method 8.2 Improvements on the Euler Method 8.3 The RungeKutta Method 8.4 Multistep Methods 8.5 More on Errors; Stability 8.6 Systems of First Order Equations
Chapter 9 Nonlinear Differential Equations and Stability 9.1 The Phase Plane: Linear Systems 9.2 Autonomous Systems and Stability 9.3 Locally Linear Systems 9.4 Competing Species 9.5 PredatorPrey Equations 9.6 Liapunov's Second Method 9.7 Periodic Solutions and Limit Cycles 9.8 Chaos and Strange Attractors: The Lorenz Equations
Chapter10 Partial Differential Equations and Fourier Series 10.1 TwoPoint Boundary Value Problems 10.2 Fourier Series 10.3 The Fourier Convergence Theorem 10.4 Even and Odd Functions 10.5 Separation of Variables; Heat Conduction in a Rod 10.6 Other Heat Conduction Problems 10.7 The Wave Equation: Vibrations of an Elastic String 10.8 Laplace's Equation Appendix A Derivation of the Heat Conduction Equation Appendix B Derivation of the Wave Equation
Chapter 11 Boundary Value Problems and SturmLiouville Theory 11.1 The Occurrence of TwoPoint Boundary Value Problems 11.2 SturmLiouville Boundary Value Problems 11.3 Nonhomogeneous Boundary Value Problems 11.4 Singular SturmLiouville Problems 11.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion 11.6 Series of Orthogonal Functions: Mean Convergence Answers to Problems Index



William E. Boyce, Rensselaer Polytechnic Institute


