(Ebook PDF) Fundamentals of Advanced Mathematics V3 1st edition by Henri Bourles 0081023863 9780081023860 full chapters

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ISBN-10 :  0081023863 

ISBN-13 :  9780081023860

Author: Henri Bourles 

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.

Fundamentals of Advanced Mathematics V3 1st Table of contents:

1: Differential Calculus
Abstract
1.1 Introduction
1.2 Fréchet differential calculus
1.3 Other approaches to differential calculus
1.4 Smooth partitions of unity
1.5 Ordinary differential equations
2: Differential and Analytic Manifolds
Abstract
2.1 Introduction
2.2 Manifolds: tangent space of a manifold at a point
2.3 Tangent linear mappings; submanifolds
2.4 Lie groups and their actions
3: Fiber Bundles
Abstract
3.1 Introduction
3.2 Tangent bundle and cotangent bundle
3.3 Fibrations
3.4 Vector bundles
3.5 Principal bundles
4: Tensor Calculus on Manifolds
Abstract
4.1 Introduction
4.2 Tensor calculus
4.3 Tensor fields
4.4 Differential forms
4.5 Pseudo-Riemannian manifolds
5: Differential and Integral Calculus on Manifolds
Abstract
5.1 Introduction
5.2 Currents and differential operators
5.3 Manifolds of mappings
5.4 Lie derivatives
5.5 Exterior differential
5.6 Stokes’ formula and applications
5.7 Integral curves and manifolds
6: Analysis on Lie Groups
Abstract
6.1 Introduction
6.2 Convolution
6.3 Classification of Lie algebras
6.4 Relation between Lie groups and Lie algebras
6.5 Harmonic analysis
7: Connections
Abstract
7.1 Introduction
7.2 Linear connections
7.3 Method of moving frames
7.4 Riemannian geometry

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