Titlebook: Vector Calculus; Paul C. Matthews Textbook 1998 Springer-Verlag London 1998 Vector calculus.algebra.applied mathematics.calculus.dynamics.

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Line, Surface and Volume Integrals,icated types of integration, however, it is useful to review the concept of integration and some standard techniques for evaluating integrals. It is important that the reader is familiar with these methods, since this will be assumed in the following sections.

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Curvilinear Coordinates,to use. Consider, for example, the problem of finding the electric field produced by a charged sphere. In this chapter the general theory of non-Cartesian coordinate systems is introduced. Formulae for grad, div and curl in these coordinate systems are developed and the two most important examples,

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Cartesian Tensors, precise mathematical statement is developed, using the idea that the physical quantity exists independently of any coordinate system that may be used. This new mathematical definition of vectors and scalars is generalised to define a wider class of objects known as tensors. Throughout this chapter

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Applications of Vector Calculus, is the subject of numerous books and a great deal of current research, so it is not possible to go into any detail in this book. However, a number of important governing equations and results can be obtained using the methods described in the previous chapters. In particular, it will be seen that t

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