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Line Integrals and Double Integrals
1991We have already met functions and vector functions of one variable, and functions of two or more variables. We now look briefly at vector functions of two or three variables. When the domain of such functions is a region of space, we usually refer to the functions as vector fields.
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Double Series and Improper Double Integrals
2009In this chapter, we shall develop the theory of double sequences, double series, and improper double integrals. Our treatment will be analogous to the treatment of sequences, series, and improper integrals of functions of one variable given in Chapter 9 of ACICARA. Much of this chapter can be read independently of the previous chapters of this book.
Sudhir R. Ghorpade, Balmohan V. Limaye
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2010
Although the definition of the integral reflects its origins in scientific problems, its evaluation relies on a considerable range of mathematical concepts and tools. Most fundamental is the change of variables formula; the single-variable version (“u-substitution”) is perhaps the core technique of integration in the introductory calculus course.
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Although the definition of the integral reflects its origins in scientific problems, its evaluation relies on a considerable range of mathematical concepts and tools. Most fundamental is the change of variables formula; the single-variable version (“u-substitution”) is perhaps the core technique of integration in the introductory calculus course.
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INDEPENDENCE OF DOUBLE WIENER INTEGRALS
Econometric Theory, 2001In this paper a necessary and sufficient condition is obtained for two double Wiener integrals to be statistically independent, first in the case of symmetric and continuous kernels. It is also shown that, for more than two double Wiener integrals, pairwise independence implies mutual independence.
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Double Integrals, Triple Integrals, and Line Integrals
2008This chapter is devoted to presenting some results on double integrals, triple integrals, n-fold integrals, and line integrals.
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