Merry, W. J.

[2026]
Springer Nature Cham
ISBN: 9783032037329

Cham : Springer Nature xvii, 393 pages : illustrations ([2026])[2026]  

Abstract: Chapter 1. Smooth manifolds -- Chapter 2. Tangent spaces -- Chapter 3. Partition of unity -- Chapter 4. The derivative -- Chapter 5. The tangent bundle -- Chapter 6. Submanifolds -- Chapter 7. The Whitney theorems -- Chapter 8. Vector fields -- Chapter 9. Flows -- Chapter 10. Lie groups -- Chapter 11. The Lie algebra of a Lie group -- Chapter 12. Smooth actions of Lie groups -- Chapter 13. Homogeneous spaces -- Chapter 14. Distributions and integrability -- Chapter 15. Foliations and the Frobenius theorem -- Chapter 16. Bundles -- Chapter 17. The fibre bundle construction theorem -- Chapter 18. Associated bundles -- Chapter 19. Tensor and exterior algebras -- Chapter 20. Sections of vector bundles -- Chapter 21. Tensor fields -- Chapter 22. The Lie derivative revisited -- Chapter 23. The exterior differential -- Chapter 24. Orientations and manifolds with boundary -- Chapter 25. Smooth singular cubes -- Chapter 26. Stokes' theorem -- Chapter 27. The Poincaré lemma and the de Rham theorem

Keyword(s): Geometry, Differential (LCSH)