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Thinking About Ordinary Differential Equations

By: Material type: TextTextSeries: Cambridge texts in applied mathematicsPublication details: Cambridge: Cambridge University Press, 1997.Description: x, 247 pages : illustrationsISBN:
  • 9780521557429
  • 0521557429
  • 9780521553148
  • 0521553148
Subject(s): DDC classification:
  • 515.352 OMA
Contents:
1. First-order equations -- 2. Linear second-order equations -- 3. Power series solutions and special functions -- 4. Systems of linear differential equations -- 5. Stability concepts -- 6. Singular perturbation methods.
Summary: Ordinary differential equations - the building blocks of mathematical modelling - are also key elements of disciplines as diverse as engineering and economics. Although mastery of these equations is essential, adhering to any one method of solving them is not: This book stresses alternative examples and analyses by means of which the student can build an understanding of a number of approaches to finding solutions and understanding their behavior. The text includes brief expositions of standard topics, including first-order equations, homogeneous and nonhomogeneous second-order linear equations, power series expansions about regular and regular singular points, linear systems theory, and stability concepts for both the phase plane and higher-dimensional systems. A variety of exercises and examples is included, and readers are encouraged to try alternative approaches to find solutions that integrate and build upon ideas introduced in earlier chapters. This book offers not only an applied perspective for the student learning to solve differential equations, but also the challenge to apply these analytical tools in the context of singular perturbations, which arises in many areas of application. An important resource for the advanced undergraduate, this book would be equally useful for the beginning graduate student investigating further approaches to these essential equations
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Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
Reference Books Reference Books Main Library Reference Reference 515.352 OMA (Browse shelf(Opens below)) Available 008755
Total holds: 0

Index

1. First-order equations --
2. Linear second-order equations --
3. Power series solutions and special functions --
4. Systems of linear differential equations --
5. Stability concepts --
6. Singular perturbation methods.

Ordinary differential equations - the building blocks of mathematical modelling - are also key elements of disciplines as diverse as engineering and economics. Although mastery of these equations is essential, adhering to any one method of solving them is not: This book stresses alternative examples and analyses by means of which the student can build an understanding of a number of approaches to finding solutions and understanding their behavior. The text includes brief expositions of standard topics, including first-order equations, homogeneous and nonhomogeneous second-order linear equations, power series expansions about regular and regular singular points, linear systems theory, and stability concepts for both the phase plane and higher-dimensional systems. A variety of exercises and examples is included, and readers are encouraged to try alternative approaches to find solutions that integrate and build upon ideas introduced in earlier chapters. This book offers not only an applied perspective for the student learning to solve differential equations, but also the challenge to apply these analytical tools in the context of singular perturbations, which arises in many areas of application. An important resource for the advanced undergraduate, this book would be equally useful for the beginning graduate student investigating further approaches to these essential equations

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