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Scientific computing with Mathematica : mathematical problems for ordinary differential equations / Addolorata Marasco and Antonio Romano.

By: Contributor(s): Material type: TextTextSeries: Modeling and simulation in science, engineering and technologyPublication details: Boston : Birkhauser, ©2001.Description: xiv, 270 p. : ill. ; 25 cm. + 1 computer optical disc (4 3/4 in.)ISBN:
  • 9780817642051
Subject(s): DDC classification:
  • 515.350285 23 M311
Contents:
1 Solutions of ODEs and Their Properties 1 -- 1.2 Definitions and Existence Theory 5 -- 1.3 Functions DSolve, NDSolve, and DifferentialInvariants 8 -- 1.4 Phase Portrait 12 -- 1.5 Applications of the Programs Sysn, Phase2D, PolarPhase, and Phase3D 15 -- 2 Linear ODEs with Constant Coefficients 33 -- 2.2 General Solution of Linear Differential Systems with Constant Coefficients 35 -- 2.3 Program LinSys 37 -- 3 Power Series Solutions of ODEs and Frobenius Series 49 -- 3.2 Power Series and the Program Taylor 50 -- 3.3 Power Series and Solutions of ODEs 53 -- 3.4 Series Solutions Near Regular Singular Points: Method of Frobenius 55 -- 3.5 Program SerSol 59 -- 3.6 Other Applications of SerSol 64 -- 3.7 Program Frobenius 70 -- 4 Poincare's Perturbation Method 79 -- 4.2 Poincare's Perturbation Method 80 -- 4.3 How to Introduce the Small Parameter 82 -- 4.4 Program Poincare 86 -- 5 Problems of Stability 99 -- 5.2 Definitions of Stability 100 -- 5.3 Analysis of Stability: The Direct Method 103 -- 5.4 Polynomial Liapunov Functions 107 -- 5.5 Program Liapunov 111 -- 5.6 Analysis of Stability, the Indirect Method: The Planar Case 119 -- 5.7 Program LStability 121 -- 6 Stability: The Critical Case 127 -- 6.2 Planar Case and Poincare's Method 128 -- 6.3 Programs CriticalEqS and CriticalEqN 131 -- 6.4 Center Manifold 138 -- 6.5 Program CManifold 141 -- 7 Bifurcation in ODEs 145 -- 7.1 Introduction to Bifurcation 145 -- 7.2 Bifurcation in a Differential Equation Containing One Parameter 146 -- 7.3 Programs Bif1 and Bif1G 153 -- 7.5 Bifurcation in a Differential Equation Depending on Two Parameters 158 -- 7.6 Programs Bif2 and Bif2G 164 -- 7.8 Hopf's Bifurcation 168 -- 7.9 Program HopfBif 170 -- 8 Lindstedt-Poincare Method 177 -- 8.1 Asymptotic Expansions 177 -- 8.2 Lindstedt-Poincare Method 179 -- 8.3 Programs LindPoinc and GLindPoinc 183 -- 9 Boundary-Value Problems for Second-Order ODEs 201 -- 9.1 Boundary-Value Problems and Bernstein's Theorem 201 -- 9.2 Shooting Method 204 -- 9.3 Program NBoundary 208 -- 9.4 Finite Difference Method 215 -- 9.5 Programs NBoundary1 and NBoundary2 219 -- 10 Rigid Body with a Fixed Point 231 -- 10.2 Euler's Equations 232 -- 10.3 Free Rotations or Poinsot's Motions 235 -- 10.4 Heavy Gyroscope 237 -- 10.5 Gyroscopic Effect 239 -- 10.6 Program Poinsot 241 -- 10.7 Program Solid 249 -- A How to Use the Package ODE.m 261 -- A.1 Notebooks for Using ODE.m 261 -- A.2 A Brief Introduction to Programming 261 -- A.3 Structure of Program Sysn 263.
Summary: This book is 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 of 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 ODEs 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. This book is an essential text/reference for students, graduates, and practitioners in engineering and applied mathematics interested in problems of ODEs in both the qualitative and quantitative description of solutions with the Mathematica program. It is also suitable as a self-study resource for professionals and others seeking an understanding of how to use ODEs in modeling physical, biological, and economic phenomena. Editorial Reviews - Scientific Computing with Mathematica From the Publisher Many interesting behaviors of real physical, biological, economic, 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 of ODEs and Mathematica in the dynamics of rigid bodies. Mathematical methods and scientific computation.
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Holdings
Item type Current library Call number Status Notes Date due Barcode Item holds
Books ISI Library, Kolkata 515.350285 M311 (Browse shelf(Opens below)) Available 137026
CD/DVD ISI Library, Kolkata 515.350285 M311 (Browse shelf(Opens below)) Available Accompanying with accession no. 137026 D946
Total holds: 0

CD-ROM includes: Mathematica files (ODE.m and 11 notebooks: Chapter1.nb - Chapter10.nb and Package.nb).

Includes bibliographical references and index.

1 Solutions of ODEs and Their Properties 1 --
1.2 Definitions and Existence Theory 5 --
1.3 Functions DSolve, NDSolve, and DifferentialInvariants 8 --
1.4 Phase Portrait 12 --
1.5 Applications of the Programs Sysn, Phase2D, PolarPhase, and Phase3D 15 --
2 Linear ODEs with Constant Coefficients 33 --
2.2 General Solution of Linear Differential Systems with Constant Coefficients 35 --
2.3 Program LinSys 37 --
3 Power Series Solutions of ODEs and Frobenius Series 49 --
3.2 Power Series and the Program Taylor 50 --
3.3 Power Series and Solutions of ODEs 53 --
3.4 Series Solutions Near Regular Singular Points: Method of Frobenius 55 --
3.5 Program SerSol 59 --
3.6 Other Applications of SerSol 64 --
3.7 Program Frobenius 70 --
4 Poincare's Perturbation Method 79 --
4.2 Poincare's Perturbation Method 80 --
4.3 How to Introduce the Small Parameter 82 --
4.4 Program Poincare 86 --
5 Problems of Stability 99 --
5.2 Definitions of Stability 100 --
5.3 Analysis of Stability: The Direct Method 103 --
5.4 Polynomial Liapunov Functions 107 --
5.5 Program Liapunov 111 --
5.6 Analysis of Stability, the Indirect Method: The Planar Case 119 --
5.7 Program LStability 121 --
6 Stability: The Critical Case 127 --
6.2 Planar Case and Poincare's Method 128 --
6.3 Programs CriticalEqS and CriticalEqN 131 --
6.4 Center Manifold 138 --
6.5 Program CManifold 141 --
7 Bifurcation in ODEs 145 --
7.1 Introduction to Bifurcation 145 --
7.2 Bifurcation in a Differential Equation Containing One Parameter 146 --
7.3 Programs Bif1 and Bif1G 153 --
7.5 Bifurcation in a Differential Equation Depending on Two Parameters 158 --
7.6 Programs Bif2 and Bif2G 164 --
7.8 Hopf's Bifurcation 168 --
7.9 Program HopfBif 170 --
8 Lindstedt-Poincare Method 177 --
8.1 Asymptotic Expansions 177 --
8.2 Lindstedt-Poincare Method 179 --
8.3 Programs LindPoinc and GLindPoinc 183 --
9 Boundary-Value Problems for Second-Order ODEs 201 --
9.1 Boundary-Value Problems and Bernstein's Theorem 201 --
9.2 Shooting Method 204 --
9.3 Program NBoundary 208 --
9.4 Finite Difference Method 215 --
9.5 Programs NBoundary1 and NBoundary2 219 --
10 Rigid Body with a Fixed Point 231 --
10.2 Euler's Equations 232 --
10.3 Free Rotations or Poinsot's Motions 235 --
10.4 Heavy Gyroscope 237 --
10.5 Gyroscopic Effect 239 --
10.6 Program Poinsot 241 --
10.7 Program Solid 249 --
A How to Use the Package ODE.m 261 --
A.1 Notebooks for Using ODE.m 261 --
A.2 A Brief Introduction to Programming 261 --
A.3 Structure of Program Sysn 263.

This book is 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 of 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 ODEs 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. This book is an essential text/reference for students, graduates, and practitioners in engineering and applied mathematics interested in problems of ODEs in both the qualitative and quantitative description of solutions with the Mathematica program. It is also suitable as a self-study resource for professionals and others seeking an understanding of how to use ODEs in modeling physical, biological, and economic phenomena. Editorial Reviews - Scientific Computing with Mathematica From the Publisher Many interesting behaviors of real physical, biological, economic, 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 of ODEs and Mathematica in the dynamics of rigid bodies. Mathematical methods and scientific computation.

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