Differential geometry of manifolds. (2010)

• Record Type: Book
• Further Information: Note: Stephen Lovett.
• Other Names: Lovett, Stephen (Stephen T.)
• Contents: Analysis of Multivariable Functions; Functions from Rn to Rm; Continuity, Limits, and Differentiability; Differentiation Rules: Functions of Class Cr; Inverse and Implicit Function Theorems; Coordinates, Frames, and Tensor Notation; Curvilinear Coordinates; Moving Frames in Physics; Moving Frames and Matrix Functions; Tensor Notation; Differentiable Manifolds; Definitions and Examples; Differentiable Maps between Manifolds; Tangent Spaces and Differentials; Immersions, Submersions, and Submanifolds; Chapter Summary; Analysis on Manifolds; Vector Bundles on Manifolds; Vector Fields on Manifolds; Differential Forms; Integration on Manifolds; Stokes’ Theorem; Introduction to Riemannian Geometry; Riemannian Metrics; Connections and Covariant Differentiation; Vector Fields Along Curves: Geodesics; The Curvature Tensor; Applications of Manifolds to Physics; Hamiltonian Mechanics; Electromagnetism; Geometric Concepts in String Theory; A Brief Introduction to General Relativity; Point Set Topology; Introduction; Metric Spaces; Topological Spaces; Proof of the Regular Jordan Curve Theorem; Simplicial Complexes and Triangulations; Euler Characteristic; Calculus of Variations; Formulation of Several Problems; The Euler-Lagrange Equation; Several Dependent Variables; Isoperimetric Problems and Lagrange Multipliers; Multilinear Algebra; Direct Sums; Bilinear and Quadratic Forms; The Hom Space and the Dual Space; The Tensor Product; Symmetric Product and Alternating Product; The Wedge Product and Analytic Geometry
• Publisher Details: Place of publication not identified : A K Peters/CRC Press
• Publication Date: 2010
• Extent: 1 online resource (440 pages)
• Subjects: 516.3/6; Manifolds (Mathematics); Differential geometry
• Languages: English
• ISBNs: 9781439865460; 1439865469
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.