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· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 기하학 > 미분기하학
· ISBN : 9781461478669
· 쪽수 : 302쪽
목차
Preface.- Why Tensor Calculus?.- 1. Rules of the Game.- 2. Coordinate Systems and the Role of Tensor Calculus.- 3. Change of Coordinates.- 4. _Tensor Description of Euclidean Spaces.- 5. The Tensor Property.- 6. Covariant Differentiation.- 7. Determinants and the Levi-Civita Symbol.- 8. Tensor Description of Surfaces.- 9. Covariant Derivative of Tensors with Surface Indices.- 10. The Curvature Tensor.- 11. Covariant Derivative of Tensors with Spatial Indices.- 12. Integration and Gauss's Theorem.- 13. Intrinsic Features of Embedded Surfaces.- 14. Further Topics in Differential Geometry.- 15. Classical Problems in the Calculus of Variations.- 16. Equations of Classical Mechanics.- 17. Equations of Continuum Mechanics.- 18. Einstein's Theory of Relativity.- 19. The Rules of Calculus of Moving Surfaces.- 20. Applications of the Calculus of Moving Surfaces.