John H. Hubbard, Beverly H. West

Differential Equations: A Dynamical Systems Approach (eBook, PDF)

Ordinary Differential Equations

• Format: PDF

Produktbeschreibung

This corrected third printing retains the authors'main emphasis on ordinary differential equations. It is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. The authors have taken the view that a differential equations theory defines functions; the object of the theory is to understand the behaviour of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods, and the companion software, MacMath, is designed to bring these notions to life.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 350
• Erscheinungstermin: 27. November 2013
• Englisch
• ISBN-13: 9781461209379
• Artikelnr.: 43987513

Inhaltsangabe

of Part II.- Systems of Ordinary Differential Equations The Higher-Dimensional Theory x? = f(t,x).- 6 Systems of Differential Equations.- 7 Systems of Linear Differential Equations.- 8 Systems of Nonlinear Differential Equations.- 8* Structural Stability.- 9 Bifurcations.- Appendix L: Linear Algebra.- L1 Theory of Linear Equations: In Practice.- L2 Theory of Linear Equations: Vocabulary.- L3 Vector Spaces and Inner Products.- L4 Linear Transformations and Inner Products.- L5 Determinants and Volumes.- L6 Eigenvalues and Eigenvectors.- L7 Finding Eigenvalues: The QR Method.- L8 Finding Eigenvalues: Jacobi's Method.- Appendix L Exercises.- Appendix L Summary.- Appendix T: Key Theorems From Parts I and III.- References.- Answers to Selected Problems.

Rezensionen

.H. Hubbard and B.H. West

Differential Equations: A Dynamical Systems Approach

"As attention has moved from idealized linear differential equations to the nonlinear equations of the real world, there has been a concomitant change of emphasis, even a paradigm shift, from quantitative methods, analytical and numerical, to qualitative methods. Though qualitative methods originated with Poincaré (Poincare) early in this century, the era of large-scale computation and computer graphics has spurred development through a profound confluence of theory and experiment. Hubbard and West demonstrate convincingly that it is feasible and necessary to incorporate this sophisticated viewpoint into the most elementary stages of differential equations pedagogy, even where the focus is still on linear equations. This is an unusual book in being both rigorous and squarely addressed to those students with the most practical needs. The well known exchange value between pictures andwords is thoroughly exploited to ground fundamental concepts."-CHOICE