Scientific Computing with Mathematica® : Mathematical Problems for Ordinary Differential Equations / by Addolorata Marasco, Antonio Romano
(Modeling and Simulation in Science, Engineering and Technology)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser |
| 出版年 | 2001 |
| 本文言語 | 英語 |
| 大きさ | XIV, 270 p : online resource |
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| 内容注記 | 1 Solutions of ODEs and Their Properties 1.1 Introduction 1.2 Definitions and Existence Theory 1.3 Functions DSolve, NDSolve, and Differentiallnvariants 1.4 The Phase Portrait 1.5 Applications of the Programs Sysn, Phase2D, PolarPhase, and Phase3D 1.6 Problems 2 Linear ODEs with Constant Coefficients 2.1 Introduction 2.2 The General Solution of Linear Differential Systems with Constant Coefficients 2.3 The Program LinSys 2.4 Problems 3 Power Series Solutions of ODEs and Frobenius Series 3.1 Introduction 3.2 Power Series and the Program Taylor 3.3 Power Series and Solutions of ODEs 3.4 Series Solutions Near Regular Singular Points: Method of Frobenius 3.5 The Program SerSol 3.6 Other Applications of SerSol 3.7 The Program Frobenius 3.8 Problems 4 Poincaré’s Perturbation Method 4.1 Introduction 4.2 Poincaré’s Perturbation Method 4.3 How to Introduce the Small Parameter 4.4 The Program Poincare 4.5 Problems 5 Problems of Stability 5.1 Introduction 5.2 Definitions of Stability 5.3 Analysis of Stability: The Direct Method 5.4 Polynomial Liapunov Functions 5.5 The Program Liapunov 5.6 Analysis of Stability, the Indirect Method: The Planar Case 5.7 The Program LStability 5.8 Problems 6 Stability: The Critical Case 6.1 Introduction 6.2 The Planar Case and Poincaré’s Method 6.3 The Programs CriticalEqS and CriticalEqN 6.4 The Center Manifold 6.5 The Program CManifold 6.6 Problems 7 Bifurcation in ODEs 7.1 Introduction to Bifurcation 7.2 Bifurcation in a Differential Equation Containing One Parameter 7.3 The Programs Bifl and Bif1G 7.4 Problems 7.5 Bifurcation in a Differential Equation Depending on Two Parameters 7.6 The Programs Bif2 and Bif2G 7.7 Problems 7.8 Hopf’s Bifurcation 7.9 The Program HopfBif 7.10 Problems 8 The Lindstedt-Poincaré Method 8.1 Asymptotic Expansions 8.2 The Lindstedt-Poincaré Method 8.3 The Programs LindPoinc and GLindPoinc 8.4 Problems 9 Boundary-Value Problems for Second-Order ODEs 9.1 Boundary-Value Problems and Bernstein’s Theorem 9.2 The Shooting Method 9.3 The Program NBoundary 9.4 The Finite Difference Method 9.5 The Programs NBoundaryl and NBoundary2 9.6 Problems 10 Rigid Body with a Fixed Point 10.1 Introduction 10.2 Euler’s Equations 10.3 Free Rotations or Poinsot’s Motions 10.4 Heavy Gyroscope 10.5 The Gyroscopic Effect 10.6 The Program Poinsot 10.7 The Program Solid 10.8 Problems A How to Use the Package ODE.m References |
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| 一般注記 | Many interesting behaviors of real physical, biological, economical, and chemical systems can be described by ordinary differential equations (ODEs). Scientific Computing with Mathematica for Ordinary Differential Equations provides a general framework useful for the applications, on the conceptual aspects of the theory of ODEs, as well as a sophisticated use of Mathematica software for the solutions of problems related to ODEs. In particular, a chapter is devoted to the use ODEs and Mathematica in the Dynamics of rigid bodies. Mathematical methods and scientific computation are dealt with jointly to supply a unified presentation. The main problems of ordinary differential equations such as, phase portrait, approximate solutions, periodic orbits, stability, bifurcation, and boundary problems are covered in an integrated fashion with numerous worked examples and computer program demonstrations using Mathematica. Topics and Features:*Explains how to use the Mathematica package ODE.m to support qualitative and quantitative problem solving *End-of- chapter exercise sets incorporating the use of Mathematica programs *Detailed description and explanation of the mathematical procedures underlying the programs written in Mathematica *Appendix describing the use of ten notebooks to guide the reader through all the exercises. This book is an essential text/reference for students, graduates and practitioners in applied mathematics and engineering interested in ODE's problems in both the qualitative and quantitative description of solutions with the Mathematica program. It is also suitable as a self- |
| 著者標目 | *Marasco, Addolorata author Romano, Antonio author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Mathematical analysis LCSH:Analysis (Mathematics) LCSH:Differential equations LCSH:Applied mathematics LCSH:Engineering mathematics LCSH:Computer mathematics LCSH:Computer software LCSH:Mathematical models FREE:Mathematics FREE:Mathematical Modeling and Industrial Mathematics FREE:Analysis FREE:Mathematical Software FREE:Ordinary Differential Equations FREE:Computational Science and Engineering FREE:Applications of Mathematics |
| 分 類 | DC23:003.3 |
| 巻冊次 | ISBN:9781461201519 
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| ISBN | 9781461201519 |
| URL | http://dx.doi.org/10.1007/978-1-4612-0151-9 |
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