Hill’s Equation (Dover Books on Mathematics) by Wilhelm Magnus (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐If you are looking for the reprint of classical work of Wilhelm Magnus and Stanley Winkler on the Hill’s Equation this is not the one. Note that the title of this book is “Hills Equation” which clearly shows how much the “publisher” knows about Hill’s equation. This “book” is 20 pages photo copy of the Wilhelm Magnus and Abe Shneitzer research report. The quality of the print renders report unreadable. Content is irrelevant anyway.

⭐The book is a classical work on this very specific topic and contains a summary which is understandable to the layman of nearly one century of work on those equations. It is a very good start to follow more recent work on that topic

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