Higher order derivatives
- Mukhopadhyay, Satya N.
- Boca Raton, FL : CRC Press, c2012.
- Physical description
- xv, 204 p. : ill ; 25 cm.
- Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ; 144.
QA325 .M85 2012
- Unknown QA325 .M85 2012
- Includes bibliographical references (p. 187-198) and index.
- Introduction Higher order derivatives Divided difference of order n General derivatives of order n Generalized Riemann derivatives of order n Peano derivatives Riemann* derivatives Symmetric de la Vallee Poussin derivatives Symmetric Riemann* derivatives Cesaro derivatives Symmetric Cesaro derivatives Borel derivatives Symmetric Borel derivatives Lp-derivatives Symmetric Lp-derivatives Abel derivatives Laplace derivatives Symmetric Laplace derivatives Relations between derivatives Ordinary and Peano derivatives Riemann* and Peano derivatives Symmetric Riemann* and symmetric de la Vallee Poussin derivatives Cesaro and Peano derivatives Peano and symmetric de la Vallee Poussin derivatives and smoothness of order k Symmetric Cesaro and symmetric de la Vallee Poussin derivatives Borel and Peano derivatives Symmetric Borel and symmetric de la Vallee Poussin derivatives Borel and symmetric Borel derivatives and Borel smoothness of order k Peano and Lp-derivatives Lp- and symmetric Lp-derivatives Symmetric de la Vallee Poussin and symmetric Lp-derivatives Borel and Lp-derivatives Symmetric Borel and symmetric Lp-derivatives Cesaro and Borel derivatives Symmetric Cesaro and symmetric Borel derivatives Abel and symmetric de la Vallee Poussin derivatives Laplace, Peano and generalized Peano derivatives Laplace and Borel derivatives Symmetric Laplace and symmetric de la Vallee Poussin derivatives Laplace and symmetric Laplace derivatives Peano and the unsymmetric Riemann derivatives Symmetric de la Vallee Poussin and the symmetric Riemann derivatives Generalized Riemann and Peano derivatives MZ- and Peano derivatives.
- (source: Nielsen Book Data)
- Publisher's Summary
- 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.
(source: Nielsen Book Data)
- Publication date
- Satya N. Mukhopadhyay.
- Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ; 144