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by Witold Hurewicz

Download Lectures on Ordinary Differential Equations fb2, epub

ISBN: 0262580012
Author: Witold Hurewicz
Language: English
Publisher: The MIT Press (March 15, 1964)
Pages: 122
Category: Mathematics
Subcategory: Science
Rating: 4.7
Votes: 626
Size Fb2: 1516 kb
Size ePub: 1250 kb
Size Djvu: 1148 kb
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Subsequent chapters address systems of differential equations, linear systems of differential equations . Witold Hurewicz (1904–56) was Professor of Mathematics at MIT for more than 20 years.

Subsequent chapters address systems of differential equations, linear systems of differential equations, singularities of an autonomous system, and solutions of an autonomous system in the large. See every Dover book in print at ww. overpublications.

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Among ordinary differential equations, linear differential equations play .

Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathematics are solutions of linear differential equations (see Holonomic function). Witold Hurewicz, Lectures on Ordinary Differential Equations, Dover Publications, ISBN 0-486-49510-8. Ibragimov, Nail H (1993). Hazewinkel, Michiel, ed.

His mother was Katarzyna Finkelsztain who hailed from Biała Cerkiew, a town that belonged to the Kingdom of Poland until the Second Partition of Poland (1793) when it was taken by Russia. Lectures on ordinary differential equations is an introduction to ordinary differential equations that again reflects the clarity of his thinking and the quality of his writing.

Download books for free. A rigorous and lively introduction. Download (djvu, 822 Kb) Donate Read.

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Start by marking Lectures on Ordinary Differential Equations as Want to Read: Want to Read savin. ant to Read. Witold Hurewicz was a world-class mathematician whose untimely death in 1956 deprived the mathematics community of one of its leading lights. His contributions to dimension theory, homotopy and other topics are outlined by Professor Solomon Lefschetz in a prefatory article "Witold Hurewicz in Memoriam" included in this volume. Also included is a list of books on differential equations for those interested in further reading, and a bibliography of Hurewicz's published works.

series Dover Books on Mathematics. Subsequent chapters address systems of differential equations, linear systems of differential equations, singularities of an autonomous system, and solutions of an autonomous system in the large.

Witold Hurewicz (author). Please provide me with your latest book news, views and details of Waterstones’ special offers.

Differential Equations WITOLD HUREWICZ 1111111 THE .

Lectures on Ordinary Differential Equations WITOLD HUREWICZ 1111111 THE . This book or any part thereof must not be reproduced in any form without the written permission of the publisher. Ix x WITOLD HUREWICZ IN MEMORIAM Mathematically Hurewicz will best be remembered for his important contributions to dimension, and above all as the founder of homotopy group theory.

Автор: Hurewicz, Witold Название: Lectures on Ordinary Differential Equations Издательство: Dover .

The book contains two exceptional chapters: one on series methods of solving differential equations, the second on numerical methods of solving differential equations.

"A rigorous and lively introduction . . . careful and lucid . . ."--The American Mathematical Monthly. Excellent hardcover edition. This concise and idea-rich introduction to a topic of perennial interest in mathematics is written so clearly and lucidly, it is well within the reach of senior mathematics students. It covers mainly existence theorems for first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. Throughout, the emphasis is on geometric methods. Witold Hurewicz was a world-class mathematician whose untimely death in 1956 deprived the mathematics community of one of its leading lights. His contributions to dimension theory, homotopy and other topics are outlined by Professor Solomon Lefschetz in a prefatory article "Witold Hurewicz in Memoriam" included in this volume. Also included is a list of books on differential equations for those interested in further reading, and a bibliography of Hurewicz's published works. Unabridged Dover republication of the work originally published by MIT Press, 1958. Prefatory article "Witold Hurewicz in Memoriam" by Solomon Lefschetz. List of References. Index. 26 figures.

Comments:

Fek
Hurewicz's modern approach to ODE theory has one very surprising aspect. His existence theory is almost all based on the Peano approximation method, not the more popular Picard iteration method. (See Hurewicz pages 1-18 and 23-33 for the Peano method, and pages 18-22 for the Picard method.) This is even more surprising when you consider Hurewicz's strong reputation in abstract combinatorial topology.

The old Peano method is typically considered not even worth mentioning in most ODE books, both old and modern. But during WW2, Hurewicz helped out with secret research on servomechanisms for the military, and this book was originally composed in 1943. (See wikipedia for details of his life.) So maybe these lectures arose somehow from that very practical work, which would have been easier with the Peano method because of the lack of computers at that time. (Hurewicz calls the Peano method the "Cauchy-Euler method".)

This is the only book I know of which presents the Peano existence method in such detail in a modern way. Hurewicz uses vector and matrix notations, which were still new at the time. The only other detailed presentation of the Peano method I know of is Murray/Miller, "Existence Theorems for Ordinary Differential Equations", pages 21-35, which is very old-fashioned.

The uniqueness theory in this book is fairly standard, based on the Lipschitz condition for the force function, but it is done in a modern elegant fashion. (The ODE presentation by Serge Lang, "Fundamentals of Differential Geometry", pages 67-88 is very modern and elegant, but is perhaps just a bit too abstract!)

In Chapter 3, Hurewicz presents linear systems of ODEs, which have great practical importance in applications. He uses matrix notations to present the special form of solutions for this class of ODEs. He starts with homogeneous linear ODEs, which are of particular interest to me because they are directly applicable to the existence of parallel transport for affinely connected manifolds.

Chapter 4 on "singularities of an autonomous system" sounds very much related to the servomechanism work which Hurewicz did, but he presents only two-dimensional cases. (When I was an undergraduate, this kind of theory was applied to dynamic systems such as population dynamics.)

This book has all of the existence and uniqueness theory which is required for two important differential geometry applications. The first is parallel transport for general connections on differentiable fiber bundles. The second is the flows (i.e. integral curves) of vector fields on manifolds, including Lie groups in particular.

Conclusion:
This is a compact introduction to the Peano approximation method for ODE existence theory, using modern notation and concepts, followed by an elegant presentation of linear systems of ODEs, and then finally two chapters on basic autonomous systems.
Acebiolane
Hurewicz was a seminal topologist, and also a very good analyst, so the Poincare-Bendixson theorem presented in the text is a perfect topic for him. The book is based on notes from a course of his.

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