Fundamentals of Advanced Mathematics V3

Henri Bourles (Conservatoire National des Arts et Metiers, France)

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English

ISTE Press Ltd - Elsevier Inc
18 September 2019

Probability & statistics; Applied mathematics; Stochastics

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.

By: Henri Bourles (Conservatoire National des Arts et Metiers France)
Imprint: ISTE Press Ltd - Elsevier Inc
Country of Publication: United Kingdom
Dimensions: Height: 229mm, Width: 151mm,
Weight: 800g
ISBN: 9781785482502
ISBN 10: 1785482505
Pages: 424
Publication Date: 18 September 2019
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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

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

Reviews for Fundamentals of Advanced Mathematics V3

"""The present volume is the third one of a series which presents the fundamental elements of advanced mathematics that is at the basis of a number of contemporary scientific methods. More precisely, it deals with differential and integral calculus in their local and global components. The book is designed not only for mathematicians, but also for everyone who uses mathematics and needs to understand the control of nonlinear systems (in particular physicists and engineers). The ambitious goal is achieved also thanks to an excellent organization of the topics and the use of a very clear and understandable language. Interesting short historical notes introduce the different topics and help to frame the evolution of concept. The exposition is illustrated with some figures that help a lot in understanding the not easy topics. Very useful attachments are provided: a careful list of notation and term indeces, a reach bibliography, a list of cited authors with biographical notes."" --ZBMath"