Fundamentals of Advanced Mathematics V3

Erscheinungsjahr 2019
ISBN: 978-1-78548-250-2
Verlag: ISTE Press Ltd - Elsevier Inc

Buch, Englisch, 424 Seiten, Format (B × H): 152 mm x 228 mm, Gewicht: 800 g

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.

Zielgruppe

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.

Autoren/Hrsg.

Bourles, Henri

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik

Inhaltsverzeichnis

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

Über Autor(innen)

Bourles, Henri
Henri Bourlès is Full Professor and Chair at the Conservatoire National des Arts et Métiers, Paris, France.