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The concept of higher order derivatives is useful in many branches
of mathematics and its applications. As they are useful in many
places, nth order derivatives are often defined directly. Higher
Order Derivatives discusses these derivatives, their uses, and the
relations among them. It covers higher order generalized
derivatives, including the Peano, d.l.V.P., and Abel derivatives;
along with the symmetric and unsymmetric Riemann, Cesaro, Borel,
LP-, and Laplace derivatives. Although much work has been done on
the Peano and de la Vallee Poussin derivatives, there is a large
amount of work to be done on the other higher order derivatives as
their properties remain often virtually unexplored. This book
introduces newcomers interested in the field of higher order
derivatives to the present state of knowledge. Basic advanced real
analysis is the only required background, and, although the special
Denjoy integral has been used, knowledge of the Lebesgue integral
should suffice.
The concept of higher order derivatives is useful in many branches
of mathematics and its applications. As they are useful in many
places, nth order derivatives are often defined directly. Higher
Order Derivatives discusses these derivatives, their uses, and the
relations among them. It covers higher order generalized
derivatives, including the Peano, d.l.V.P., and Abel derivatives;
along with the symmetric and unsymmetric Riemann, Cesaro, Borel,
LP-, and Laplace derivatives. Although much work has been done on
the Peano and de la Vallee Poussin derivatives, there is a large
amount of work to be done on the other higher order derivatives as
their properties remain often virtually unexplored. This book
introduces newcomers interested in the field of higher order
derivatives to the present state of knowledge. Basic advanced real
analysis is the only required background, and, although the special
Denjoy integral has been used, knowledge of the Lebesgue integral
should suffice.
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