Differential calculus, tensor calculus, differential geometry, global analysis
Author(s)
Bibliographic Information
Differential calculus, tensor calculus, differential geometry, global analysis
（New mathematical methods, systems and applications set / coordinated by Henri Bourlès, . Fundamentals of advanced mathematics ; 3）
ISTE Press , Elsevier, 2019
Available at / 1 libraries
-
No Libraries matched.
- Remove all filters.
Note
Includes bibliographical references (p. [369]-378) and index
Description and Table of Contents
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.
Table of Contents
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
by "Nielsen BookData"