Buch, Englisch, 440 Seiten, Format (B × H): 196 mm x 241 mm, Gewicht: 923 g
Reihe: Textbooks in Mathematics
Buch, Englisch, 440 Seiten, Format (B × H): 196 mm x 241 mm, Gewicht: 923 g
Reihe: Textbooks in Mathematics
ISBN: 978-1-56881-457-5
Verlag: Taylor & Francis Inc
Differential Geometry of Manifolds takes a practical approach, containing extensive exercises and focusing on applications of differential geometry in physics, including the Hamiltonian formulation of dynamics (with a view toward symplectic manifolds), the tensorial formulation of electromagnetism, some string theory, and some fundamental concepts in general relativity.
Autoren/Hrsg.
Weitere Infos & Material
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