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This text discusses the qualitative properties of dynamical systems including both differential equations and maps. The approach taken relies heavily on examples--supported by extensive exercises, hints to solutions, and diagrams--to develop the material, including a treatment of chaotic behavior. The unprecedented popular interest shown in recent years in the chaotic behavior of discrete dynamic systems including such topics as chaos and fractals has had its impact on the undergraduate and graduate curriculum. However there has, until now, been no text which sets out this developing area of mathematics within the context of standard teaching of ordinary differential equations.
From the Back Cover
This text discusses the qualitative properties of dynamical systems including both differential equations and maps. The approach taken relies heavily on examples (supported by extensive exercises, hints to solutions and diagrams) to develop the material, including a treatment of chaotic behavior.
The unprecedented popular interest shown in recent years in the chaotic behavior of discrete dynamic systems including such topics as chaos and fractals has had its impact on the undergraduate and graduate curriculum. However there has, until now, been no text which sets out this developing area of mathematics within the context of standard teaching of ordinary differential equations.
Applications in physics, engineering, and geology are considered and introductions to fractal imaging and cellular automata are given.
This text discusses the qualitative properties of dynamical systems including both differential equations and maps. The approach taken relies heavily on examples--supported by extensive exercises, hints to solutions, and diagrams--to develop the material, including a treatment of chaotic behavior. The unprecedented popular interest shown in recent years in the chaotic behavior of discrete dynamic systems including such topics as chaos and fractals has had its impact on the undergraduate and graduate curriculum. However there has, until now, been no text which sets out this developing area of mathematics within the context of standard teaching of ordinary differential equations.
From the Back Cover
This text discusses the qualitative properties of dynamical systems including both differential equations and maps. The approach taken relies heavily on examples (supported by extensive exercises, hints to solutions and diagrams) to develop the material, including a treatment of chaotic behavior.
The unprecedented popular interest shown in recent years in the chaotic behavior of discrete dynamic systems including such topics as chaos and fractals has had its impact on the undergraduate and graduate curriculum. However there has, until now, been no text which sets out this developing area of mathematics within the context of standard teaching of ordinary differential equations.
Applications in physics, engineering, and geology are considered and introductions to fractal imaging and cellular automata are given.
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First Sentence
In this chapter we illustrate the qualitative approach to differential equations and introduce some key ideas such as phase portraits and qualitative equivalence. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
In this chapter we illustrate the qualitative approach to differential equations and introduce some key ideas such as phase portraits and qualitative equivalence. Read the first page
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Concordance
Browse Sample PagesConcordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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