By Gerd Rudolph
Starting from an undergraduate point, this booklet systematically develops the fundamentals of
• Calculus on manifolds, vector bundles, vector fields and differential forms,
• Lie teams and Lie workforce actions,
• Linear symplectic algebra and symplectic geometry,
• Hamiltonian platforms, symmetries and relief, integrable structures and Hamilton-Jacobi theory.
The issues indexed less than the 1st merchandise are appropriate for nearly all components of mathematical physics. the second one and 3rd goods represent the hyperlink among summary calculus and the speculation of Hamiltonian platforms. The last thing presents an advent to varied elements of this idea, together with Morse households, the Maslov classification and caustics.
The ebook courses the reader from effortless differential geometry to complex themes within the concept of Hamiltonian structures with the purpose of creating present examine literature obtainable. the fashion is that of a mathematical textbook,with complete proofs given within the textual content or as routines. the cloth is illustrated through quite a few distinct examples, a few of that are taken up a number of occasions for demonstrating how the tools evolve and interact.
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