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Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations

2000 Mathematics
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Release : 2000
Genre : Mathematics
Kind : eBook
Book Rating : 901/5 ( reviews)

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Book Synopsis Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations by : Werner Balser

Download or read book Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations written by Werner Balser. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt: Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series.

Ordinary Differential Equations and Linear Algebra

2015-11-17 Mathematics
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Release : 2015-11-17
Genre : Mathematics
Kind : eBook
Book Rating : 097/5 ( reviews)

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Book Synopsis Ordinary Differential Equations and Linear Algebra by : Todd Kapitula

Download or read book Ordinary Differential Equations and Linear Algebra written by Todd Kapitula. This book was released on 2015-11-17. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary differential equations (ODEs) and linear algebra are foundational postcalculus mathematics courses in the sciences. The goal of this text is to help students master both subject areas in a one-semester course. Linear algebra is developed first, with an eye toward solving linear systems of ODEs. A computer algebra system is used for intermediate calculations (Gaussian elimination, complicated integrals, etc.); however, the text is not tailored toward a particular system. Ordinary Differential Equations and Linear Algebra: A Systems Approach systematically develops the linear algebra needed to solve systems of ODEs and includes over 15 distinct applications of the theory, many of which are not typically seen in a textbook at this level (e.g., lead poisoning, SIR models, digital filters). It emphasizes mathematical modeling and contains group projects at the end of each chapter that allow students to more fully explore the interaction between the modeling of a system, the solution of the model, and the resulting physical description.

Linear Systems of Ordinary Differential Equations, with Periodic and Quasi-Periodic Coefficients

1966-01-01 Computers
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Release : 1966-01-01
Genre : Computers
Kind : eBook
Book Rating : 355/5 ( reviews)

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Book Synopsis Linear Systems of Ordinary Differential Equations, with Periodic and Quasi-Periodic Coefficients by : Erugin

Download or read book Linear Systems of Ordinary Differential Equations, with Periodic and Quasi-Periodic Coefficients written by Erugin. This book was released on 1966-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Linear Systems of Ordinary Differential Equations, with Periodic and Quasi-Periodic Coefficients

Ordinary Differential Equations and Dynamical Systems

2012-08-30 Mathematics
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Release : 2012-08-30
Genre : Mathematics
Kind : eBook
Book Rating : 283/5 ( reviews)

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Book Synopsis Ordinary Differential Equations and Dynamical Systems by : Gerald Teschl

Download or read book Ordinary Differential Equations and Dynamical Systems written by Gerald Teschl. This book was released on 2012-08-30. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.

Ordinary Differential Equations

2013-03-11 Mathematics
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Release : 2013-03-11
Genre : Mathematics
Kind : eBook
Book Rating : 014/5 ( reviews)

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Book Synopsis Ordinary Differential Equations by : Wolfgang Walter

Download or read book Ordinary Differential Equations written by Wolfgang Walter. This book was released on 2013-03-11. Available in PDF, EPUB and Kindle. Book excerpt: Based on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.

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