Fundamentals of Advanced Mathematics V3

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.

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

1. Differential and analytic manifolds
2. Fibered bundles
3. Tensor calculus on manifolds
4. Differential and integral calculus on manifolds
5. Connections
6. Calculus of variations and optimal control