By Stephanie Frank Singer
"And what's the use," inspiration Alice, "of a booklet with no photos or conversations in it?" -Lewis Carroll This e-book is written for modem undergraduate scholars - now not the best stu dents that arithmetic professors want for (and who sometimes grace our campuses), however the scholars like many the writer has taught: gifted yet ap preciating overview and reinforcement of prior direction paintings; prepared to work flat out, yet difficult context and motivation for the maths they're studying. to fit this viewers, the writer eschews density of subject matters and potency of presentation in prefer of a gentler tone, a coherent tale, digressions on mathe maticians, physicists and their notations, uncomplicated examples labored out intimately, and reinforcement of the fundamentals. Dense and effective texts play a very important position within the schooling of budding (and budded) mathematicians and physicists. This ebook doesn't presume to enhance at the classics in that style. really, it goals to supply these classics with a wide new iteration of appreciative readers. this article introduces a few easy constructs of contemporary symplectic geometry within the context of an outdated celestial mechanics challenge, the two-body challenge. We current the derivation of Kepler's legislation of planetary movement from Newton's legislation of gravitation, first within the sort of an undergraduate physics direction, and x Preface on the other hand within the language of symplectic geometry. No past publicity to symplectic geometry is needed: we introduce and illustrate all important con structs.
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