Invariant variational principles, Volume 138 (Mathematics in Science and Engineering) by John David Logan (PDF)

Description

User’s Reviews

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

⭐Dwight Neuenschwander, in his wonderful book, Emmy Noether’s Wonderful Theorem (2011) acknowledges Professor John David Logan. Upon perusing this exceptional monograph, it is easy to understand why he does so. This slim book (169 pages total) of eight chapters has a flavor all its own. I am unable to locate reviews in the usual journals, though I’m sure they must exist. Thus, I delight in offering my own perspective on this lovely tome. Thorough preparation of advanced calculus (say, Angus Taylor) will be ample prerequisite.(1) Chapter One: foundations of Calculus of Variations and Euler- Lagrange Equations. Examples, remarks, and simpler proofs sprinkle the discourse. Fourteen problems concludes the chapter, all straightforward exercises. Afterward, we enter the promised land of invariance: “Invariance properties of single integrals under transformations which depend on r-parameters.” (page 27).(2) Second chapter introduces Emmy Noether and the requisite theorem. Galilean invariance and particle mechanics provide (a lovely ten pages) segue to the third chapter (end of chapter-two problems are likewise straightforward).This brief third chapter introduces Killing’s equations applied to solution of the damped harmonic oscillator.Next, abstract but challenging: invariance of multiple integrals (six exercise-problems to conclude, happily, with hints to their solution). Comparison to Gelfand and Fomin: Calculus of Variations (chapter seven, 1963) is fruitful at this juncture. Tensors set the stage for discussion of theory of physical fields. Here, we have a highlight of the text:(3) “…Invariance considerations in field theory arise naturally from the postulates of special relativity.” (page 76).The previous four chapters are given physical motivation: Lorentz group, electromagnetic field and Heaviside-Lorentz units are utilized. Any (or should I say, every) physicist should be familiar with Logan’s crisp exposition !In fact, comparison with Akheizer: The Calculus of Variations (chapter two, 1962) at this juncture proves illuminating.Once again, thirteen exercises which concludes the chapter are (for the most part) straightforward to solve.(4) Final three chapters are considerable more challenging, although no less interesting. We are introduced to the vibrating rod as a physical example, plus the KdV Equation for expounding higher-order derivatives. We are introduced to conformal invariance. One of the exercise-problems, ” inspect the Klein-Gordon equation under special conformal transformations,” we read “…thus, Lorentz transformations are conformal transformations with conformal factor unity…” (page 139). Finally, an introduction to parameter-invariance: “….their role in geometry and relativistic mechanics is a significant one…” (page 151). A statement which is substantiated throughout the remainder of text.(5) So ends a rather unique foray under the rubric of invariance and variational principles. With its well-written prose, its clarity of exposition, its minimum of prerequisites, I can think of few monographs which are as delightful.(Logan complements the marvelous texts of Akheizer and Gelfand).A short list of references provides signpost to more detailed (and historical) material.An excellent expository monograph.Highly recommended to those with an interest in these matters.

⭐

Keywords

Free Download Invariant variational principles, Volume 138 (Mathematics in Science and Engineering) in PDF format
Invariant variational principles, Volume 138 (Mathematics in Science and Engineering) PDF Free Download
Download Invariant variational principles, Volume 138 (Mathematics in Science and Engineering) 1977 PDF Free
Invariant variational principles, Volume 138 (Mathematics in Science and Engineering) 1977 PDF Free Download
Download Invariant variational principles, Volume 138 (Mathematics in Science and Engineering) PDF
Free Download Ebook Invariant variational principles, Volume 138 (Mathematics in Science and Engineering)