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 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.
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P.C. Matthews Vector Calculus "Written for undergraduate students in mathematics, the book covers the material in a comprehensive but concise manner, combining mathematical rigor with physical insight. There are many diagrams to illustrate the physical meaning of the mathematical concepts, which essential for a full understanding of the subject." — ZENTRALBLATT MATH
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