Ordinary Differential Equations


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Bibliografische Daten
ISBN/EAN: 9781118243404
Sprache: Englisch
Umfang: 544 S., 38.07 MB
Auflage: 1. Auflage 2014
Format: EPUB
DRM: Adobe DRM


<b>Features a balance between theory, proofs, and examples and provides applications across diverse fields of study</b><p>Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory.</p><p>Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps and provides all the necessary details. Topical coverage includes:</p><ul><li><p>First-Order Differential Equations</p></li><li><p>Higher-Order Linear Equations</p></li><li><p>Applications of Higher-Order Linear Equations</p></li><li><p>Systems of Linear Differential Equations</p></li><li><p>Laplace Transform</p></li><li><p>Series Solutions</p></li><li><p>Systems of Nonlinear Differential Equations</p></li></ul><p>In addition to plentiful exercises and examples throughout, each chapter concludes with a summary that outlines key concepts and techniques. The book's design allows readers to interact with the content, while hints, cautions, and emphasis are uniquely featured in the margins to further help and engage readers.</p><p>Written in an accessible style that includes all needed details and steps, Ordinary Differential Equations is an excellent book for courses on the topic at the upper-undergraduate level. The book also serves as a valuable resource for professionals in the fields of engineering, physics, and mathematics who utilize differential equations in their everyday work.</p><p></p><p>An Instructors Manual is available upon request. Email<a href="mailto:sfriedman@wiley.com">sfriedman@wiley.com</a> for information. There is also a Solutions Manual available. The ISBN is 9781118398999.</p>


MICHAEL D. GREENBERG, PhD, is Professor Emeritus of Mechanical Engineering at the University of Delaware where he teaches courses on engineering mathematics and is a three-time recipient of the University of Delaware Excellence in Teaching Award. Greenberg's research has emphasized vortex methods in aerodynamics and hydrodynamics.


Preface viii1. First-Order Differential Equations 11.1 Motivation and Overview 11.2 Linear First-Order Equations 111.3 Applications of Linear First-Order Equations 241.4 Nonlinear First-Order Equations That Are Separable 431.5 Existence and Uniqueness 501.6 Applications of Nonlinear First-Order Equations 591.7 Exact Equations and Equations That Can Be Made Exact 711.8 Solution by Substitution 811.9 Numerical Solution by Eulers Method 872. Higher-Order Linear Equations 992.1 Linear Differential Equations of Second Order 992.2 Constant-Coefficient Equations 1032.3 Complex Roots 1132.4 Linear Independence; Existence, Uniqueness, General Solution 1182.5 Reduction of Order 1282.6 Cauchy-Euler Equations 1342.7 The General Theory for Higher-Order Equations 1422.8 Nonhomogeneous Equations 1492.9 Particular Solution by Undetermined Coefficients 1552.10 Particular Solution by Variation of Parameters 1633. Applications of Higher-Order Equations 1733.1 Introduction 1733.2 Linear Harmonic Oscillator; Free Oscillation 1743.3 Free Oscillation with Damping 1863.4 Forced Oscillation 1933.5 Steady-State Diffusion; A Boundary Value Problem 2023.6 Introduction to the Eigenvalue Problem; Column Buckling 2114. Systems of Linear Differential Equations 2194.1 Introduction, and Solution by Elimination 2194.2 Application to Coupled Oscillators 2304.3 N-Space and Matrices 2384.4 Linear Dependence and Independence of Vectors 2474.5 Existence, Uniqueness, and General Solution 2534.6 Matrix Eigenvalue Problem 2614.7 Homogeneous Systems with Constant Coefficients 2704.8 Dot Product and Additional Matrix Algebra 2834.9 Explicit Solution of x = Ax and the Matrix Exponential Function 2974.10 Nonhomogeneous Systems 3075. Laplace Transform 3175.1 Introduction 3175.2 The Transform and Its Inverse 3195.3 Applications to the Solution of Differential Equations 3345.4 Discontinuous Forcing Functions; Heaviside Step Function 3475.5 Convolution 3585.6 Impulsive Forcing Functions; Dirac Delta Function 3666. Series Solutions 3796.1 Introduction 3796.2 Power Series and Taylor Series 3806.3 Power Series Solution About a Regular Point 3876.4 Legendre and Bessel Equations 3956.5 The Method of Frobenius 4087. Systems of Nonlinear Differential Equations 4237.1 Introduction 4237.2 The Phase Plane 4247.3 Linear Systems 4357.4 Nonlinear Systems 4477.5 Limit Cycles 4637.6 Numerical Solution of Systems by Eulers Method 468Appendix A. Review of Partial Fraction Expansions 479Appendix B. Review of Determinants 483Appendix C. Review of Gauss Elimination 491Appendix D. Review of Complex Numbers and the Complex Plane 497Answers to Exercises 501

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