Hill's Equation

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Synopsis
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject."Hill's equation" connotes the class of homogeneous, linear, second order differential equations with real, periodic coefficients. This two part treatment encompasses the most pertinent, necessary information; only the theory's elementary facts are proved in full, with minimal use of sophisticated mathematics. Part I explains the basic theory: Floquet's theorem, characteristic values and intervals of stability, analytic properties of the discriminant, infinite determinants, asymptotic behavior of the characteristic values, theorems of Liapounoff and Borg, and related topics. Part II examines numerous details: elementary formulas, oscillatory solutions, intervals of stability and instability, discriminant, coexistence, and examples. Particular attention is given to stability problems and to the question of coexistence of periodic solutions.Although intended for professional mathematicians and engineers, the volume is written so clearly and vigorously that it can be recommended for graduate students and advanced undergraduates. List of Symbols and Notations. List of Theorems, Lemmas, and Corollaries. References. Index.
Copyright:
1979

Book Details

Book Quality:
Publisher Quality
ISBN-13:
9780486150291
Related ISBNs:
9780486495651
Publisher:
Dover Publications
Date of Addition:
Copyrighted By:
Wilhelm Magnus and Stanley Winkler
Adult content:
No
Language:
English
Has Image Descriptions:
No
Categories:
Nonfiction, Mathematics and Statistics
Submitted By:
Bookshare Staff
Usage Restrictions:
This is a copyrighted book.

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