Multivariable Calculus and Differential GeometryWalter de Gruyter GmbH & Co KG, 01.07.2015 - 365 Seiten This book offers an introduction to differential geometry for the non-specialist. It includes most of the required material from multivariable calculus, linear algebra, and basic analysis. An intuitive approach and a minimum of prerequisites make it a valuable companion for students of mathematics and physics. The main focus is on manifolds in Euclidean space and the metric properties they inherit from it. Among the topics discussed are curvature and how it affects the shape of space, and the generalization of the fundamental theorem of calculus known as Stokes' theorem. |
Inhalt
| 1 | |
| 57 | |
| 117 | |
4 Integration on Euclidean space | 177 |
5 Differential Forms | 221 |
6 Manifolds as metric spaces | 267 |
7 Hypersurfaces | 301 |
Appendix A | 339 |
Appendix B | 345 |
Index | 351 |
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Häufige Begriffe und Wortgruppen
a₁ B₁ boundary c₁ claim column compact consider contained continuous converges convex coordinate vector countable defined definition denote derivative diffeomorphism differentiable map dimension du¹ eigenvalues equals equation Euclidean space Exercise exists expp finite follows function f given hypersurface i-th identity implies inner product space integral curve inverse isometry isomorphism Jacobi field Lemma linear transformation manifold map ƒ matrix measure zero metric space n-dimensional neighborhood nonempty normal geodesic Notice open set orientation orthogonal orthonormal basis P₁ parallel parametrization partition plane Proof Proposition Prove radius real numbers restriction ℝn sectional curvature sequence Show smooth submanifold subset subspace Suppose t₁ tangent space Theorem unique unit normal field upper bound V₁ vanishes vector field vector space vol(B w₁ X₁ y₁