Mathematics

For one- or two-semester courses in Dynamical Systems in the department of Advanced Mathematics.

This text gives an introduction into the ideas of dynamical systems. It is divided into two parts which can be treated in either order: the first part treats the aspects coming from systems of nonlinear ordinary differential equations, and the second part is comprised of those aspects dealing with iteration of a function. Its main emphasis is on the types of behavior which nonlinear systems of differential equations can exhibit. The text assumes that students have taken courses on calculus covering both a single variable and multivariables, a course on linear algebra, and an introductory course on differential equations.

• Flexible text—Provides a text in which the two parts can be treated in either order or just one of the two parts can be treated.

  • Enables instructors to use the text in the manner in which they choose.

• Main examples in the first sections of each chapter.

  • Allows students to refer to these sections when studying the rest of the chapter.

• A wider and deeper range of theory provided—No other undergrad text is as thorough.

• An introduction to the phase portrait method—Provided early in the text.

  • Enables students to use this information to study nonlinear equations throughout the text.

• Basic numerical methods for finding solutions—Provides explicit analytic expressions for the solution of a nonlinear system of differential equations.

  • Gives students the algorithms which are used by computers when determining solutions.

• Iteration of functions—Described in Part II.

  • Provides students with more detailed coverage of the topics presented in Part I, enabling them to progress to more complicated functions.

• Extensive pedagogy—Gives practical applications, theory and proofs, and exercises for each chapter.

  • Enables students to practice what they have learned in each chapter.

(NOTE: Each chapter concludes with Applications, Theory and Proofs, and Exercises.)

Prologue: Historical Perspective.

I. SYSTEMS OF DIFFERENTIAL EQUATIONS.

II. ITERATION OF FUNCTIONS.

Dynamical Systems  (Mathematics)

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