Ordinary differential equations
著者
書誌事項
Ordinary differential equations
Wiley, c2012
- : hardback
大学図書館所蔵 全8件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
"A John Wiley & Sons, Inc., publication"
Includes index
内容説明・目次
内容説明
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.
An Instructors Manual is available upon request. Email sfriedman@wiley.com for information. There is also a Solutions Manual available. The ISBN is 9781118398999.
目次
- 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 Transform and Its Inverse 319 5.3 Applications to the Solution of Differential Equations 334 5.4 Discontinuous Forcing Functions
- Heaviside Step Function 347 5.5 Convolution 358 5.6 Impulsive Forcing Functions
- Dirac Delta Function 366 6. Series Solutions 379 6.1 Introduction 379 6.2 Power Series and Taylor Series 380 6.3 Power Series Solution About a Regular Point 387 6.4 Legendre and Bessel Equations 395 6.5 The Method of Frobenius 408 7. Systems of Nonlinear Differential Equations 423 7.1 Introduction 423 7.2 The Phase Plane 424 7.3 Linear Systems 435 7.4 Nonlinear Systems 447 7.5 Limit Cycles 463 7.6 Numerical Solution of Systems by Euler's Method 468 Appendix A. Review of Partial Fraction Expansions 479 Appendix B. Review of Determinants 483 Appendix C. Review of Gauss Elimination 491 Appendix D. Review of Complex Numbers and the Complex Plane 497 Answers to Exercises 501
「Nielsen BookData」 より