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Viser: Vector Calculus
Vector Calculus
P. C. Matthews
(2000)
Sprog: Engelsk
Detaljer om varen
- 1. Udgave
- Paperback
- Udgiver: Springer (Januar 2000)
- ISBN: 9783540761808
1.1 Vectors and scalars.-
1.2 Dot product.-
1.3 Cross product.-
1.4 Scalar triple product.-
1.5 Vector triple product.-
1.6 Scalar fields and vector fields.-
2. Line, Surface and Volume Integrals.-
2.1 Applications and methods of integration.-
2.2 Line integrals.-
2.3 Surface integrals.-
2.4 Volume integrals.-
3. Gradient, Divergence and Curl.-
3.1 Partial differentiation and Taylor series.-
3.2 Gradient of a scalar field.-
3.3 Divergence of a vector field.-
3.4 Curl of a vector field.-
4. Suffix Notation and its Applications.-
4.1 Introduction to suffix notation.-
4.2 The Kronecker delta ?ij.-
4.3 The alternating tensor ?ijk.-
4.4 Relation between ?ijk and ?ij.-
4.5 Grad, div and curl in suffix notation.-
4.6 Combinations of grad, div and curl.-
4.7 Grad, div and curl applied to products of functions.-
5. Integral Theorems.-
5.1 Divergence theorem.-
5.2 Stokes's theorem.-
6. Curvilinear Coordinates.-
6.1 Orthogonal curvilinear coordinates.-
6.2 Grad, div and curl in orthogonal curvilinear coordinate systems.-
6.3 Cylindrical polar coordinates.-
6.4 Spherical polar coordinates.-
7. Cartesian Tensors.-
7.1 Coordinate transformations.-
7.2 Vectors and scalars.-
7.3 Tensors.-
7.4 Physical examples of tensors.-
8. Applications of Vector Calculus.-
8.1 Heat transfer.-
8.2 Electromagnetism.-
8.3 Continuum mechanics and the stress tensor.-
8.4 Solid mechanics.-
8.5 Fluid mechanics.- Solutions.