By Paul Baillon

Differential Manifold is the framework of particle physics and astrophysics these days. it's important for all study physicists to be good conversant in it or even experimental physicists may be in a position to manage equations and expressions in that framework.

This publication offers a complete description of the fundamentals of differential manifold with an entire facts of any point. a wide a part of the ebook is dedicated to the elemental mathematical thoughts during which all important for the advance of the differential manifold is related and completely proved.

This e-book is self-consistent: it starts off from first rules. The mathematical framework is the set concept with its axioms and its formal good judgment. No certain wisdom is needed.

Contents:

  • Manifold:
    • Differentiable Manifold
    • Smooth Maps
    • Vector Fields on a Differentiable Manifold
    • Conventions
    • Tangent areas and Tangent Vectors
    • Coordinate Changes
    • Metric on a Differentiable Manifold
    • One-Form box and Differential
    • Tensorial Field
    • Wedge manufactured from 1-Linear types (versus Vector Fields)
    • Exterior Differential
    • Volume and critical in Differential Manifold
    • Lie Bracket
    • Bundles and Differentiable Manifold
    • Parallel Transport
    • Curvature
    • Lagrangian of the Electro-Weak Interactions
    • General Relativity
    • Notations
  • Some easy arithmetic wanted for Manifolds:
    • General Concepts
    • Real Numbers, Set
    • Euclidean Metric
    • Metric and Topology on
    • Behavior at a Point
    • Some houses of constant Maps from to
    • Continuous Maps from Topological units to
    • Derivable Function
    • Group
    • Module Over a Commutative Ring
    • Vector Spaces
    • n
    • Complex Numbers
    • Convex Subset
    • Topology on n
    • Continuous Map on n to p
    • Sequence
    • Sequence in
    • Sequence of Maps
    • Partial Derivative
    • Topology on Convex Subsets
    • Path hooked up Sets
    • Riemann imperative of Maps with Compact Support
    • Volume in n
    • Integral of a continuing Map
    • Differential Equations
    • Lebesgue Integral
    • Taylor growth of services with Derivatives
    • Exponentials
    • Polynomials
    • Useful tender Maps equipped with Exponentials
    • Eigenvectors of a Linear Transformation
  • Conventions, uncomplicated family and Symbols:
    • Logical Theory
    • Specifics Terms
    • Quantificators
    • Specifics Relations
    • Sets
    • Integers
    • Operations on Ƶ = Ƶ 0+Ƶ
    • Rational Numbers
    • Conventions

Readership: Undergraduates in particle physics, astrophysics and mathematical physics.

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