دانلود کتاب Fundamentals of advanced mathematics. 3, Differential calculus, tensor calculus, differential geometry, global analysis

Description

Fundamentals of Advanced Mathematics, Volume Three, begins with the study of differential and analytic infinite-dimensional manifolds, then progresses into fibered bundles, in particular, tangent and cotangent bundles. In addition, subjects covered include the tensor calculus on manifolds, differential and integral calculus on manifolds (general Stokes formula, integral curves and manifolds), an analysis on Lie groups, the Haar measure, the convolution of functions and distributions, and the harmonic analysis over a Lie group. Finally, the theory of connections is (linear connections, principal connections, and Cartan connections) covered, as is the calculus of variations in Lagrangian and Hamiltonian formulations.

This volume is the prerequisite to the analytic and geometric study of nonlinear systems.
Key Features

Includes sections on differential and analytic manifolds, vector bundles, tensors, Lie derivatives, applications to algebraic topology, and more
Presents an ideal prerequisite resource on the analytic and geometric study of nonlinear systems
Provides theory as well as practical information

Readership

Graduate students in Systems Theory, Robotics, Physics or Mathematics; research engineers in Automatic control and/or robotics; assistant professors and professors in Automatic control and/or robotics