Ordinary Differential Equations

The book transitions smoothly from first-order to higher-order equations, featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology. In addition to plentiful exercises and examples throughout, each chapter concludes with a summary that outlines key concepts and techniques.

Informationen zum Autor 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. Klappentext Features a balance between theory, proofs, and examples and provides applications across diverse fields of studyOrdinary 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.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: First-Order Differential Equations Higher-Order Linear Equations Applications of Higher-Order Linear Equations Systems of Linear Differential Equations Laplace Transform Series Solutions* Systems of Nonlinear Differential EquationsIn 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.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. Zusammenfassung The book transitions smoothly from first-order to higher-order equations, featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology. In addition to plentiful exercises and examples throughout, each chapter concludes with a summary that outlines key concepts and techniques. Inhaltsverzeichnis 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 Euler's 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 P...

Auteur
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.

Texte du rabat
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study 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. 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: First-Order Differential Equations Higher-Order Linear Equations Applications of Higher-Order Linear Equations Systems of Linear Differential Equations Laplace Transform Series Solutions * Systems of Nonlinear Differential Equations 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. 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.

Contenu
Preface viii 1. First-Order Differential Equations 1 1.1 Motivation and Overview 1 1.2 Linear First-Order Equations 11 1.3 Applications of Linear First-Order Equations 24 1.4 Nonlinear First-Order Equations That Are Separable 43 1.5 Existence and Uniqueness 50 1.6 Applications of Nonlinear First-Order Equations 59 1.7 Exact Equations and Equations That Can Be Made Exact 71 1.8 Solution by Substitution 81 1.9 Numerical Solution by Euler's Method 87 2. Higher-Order Linear Equations 99 2.1 Linear Differential Equations of Second Order 99 2.2 Constant-Coefficient Equations 103 2.3 Complex Roots 113 2.4 Linear Independence; Existence, Uniqueness, General Solution 118 2.5 Reduction of Order 128 2.6 Cauchy-Euler Equations 134 2.7 The General Theory for Higher-Order Equations 142 2.8 Nonhomogeneous Equations 149 2.9 Particular Solution by Undetermined Coefficients 155 2.10 Particular Solution by Variation of Parameters 163 3. Applications of Higher-Order Equations 173 3.1 Introduction 173 3.2 Linear Harmonic Oscillator; Free Oscillation 174 3.3 Free Oscillation with Damping 186 3.4 Forced Oscillation 193 3.5 Steady-State Diffusion; A Boundary Value Problem 202 3.6 Introduction to the Eigenvalue Problem; Column Buckling 211 4. Systems of Linear Differential Equations 219 4.1 Introduction, and Solution by Elimination 219 4.2 Application to Coupled Oscillators 230 4.3 N-Space and Matrices 238 4.4 Linear Dependence and Independence of Vectors 247 4.5 Existence, Uniqueness, and General Solution 253 4.6 Matrix Eigenvalue Problem 261 4.7 Homogeneous Systems with Constant Coefficients 270 4.8 Dot Product and Additional Matrix Algebra 283 4.9 Explicit Solution of x' = Ax and the Matrix Exponential Function 297 4.10 Nonhomogeneous Systems 307 5. Laplace Transform 317 5.1 Introduction 317 5.2 The Transf…