Author | Matthews, Paul C. author |
---|---|
Title | Vector Calculus [electronic resource] / by Paul C. Matthews |
Imprint | London : Springer London : Imprint: Springer, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4471-0597-8 |
Descript | X, 182 p. 1 illus. online resource |
1. Vector Algebra -- 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 Stokesโs 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