[PDF] Higher Order Derivatives eBook

Author : Satya Mukhopadhyay
Publisher : CRC Press
Page : 222 pages
File Size : 40,85 MB
Release : 2012-01-25
Category : Mathematics
ISBN : 1439880476

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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, Cesàro, Borel, LP-, and Laplace derivatives. Although much work has been done on the Peano and de la Vallée 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.

Author : Richard E. Blahut
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 14,79 MB
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 1461526949

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Information theory is an exceptional field in many ways. Technically, it is one of the rare fields in which mathematical results and insights have led directly to significant engineering payoffs. Professionally, it is a field that has sustained a remarkable degree of community, collegiality and high standards. James L. Massey, whose work in the field is honored here, embodies the highest standards of the profession in his own career. The book covers the latest work on: block coding, convolutional coding, cryptography, and information theory. The 44 contributions represent a cross-section of the world's leading scholars, scientists and researchers in information theory and communication. The book is rounded off with an index and a bibliography of publications by James Massey.

Author : Satya Mukhopadhyay
Publisher : Chapman and Hall/CRC
Page : 220 pages
File Size : 38,67 MB
Release : 2012-01-25
Category : Mathematics
ISBN : 9781439880487

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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 Pea

Author : Andreas Griewank
Publisher : SIAM
Page : 448 pages
File Size : 25,31 MB
Release : 2008-11-06
Category : Mathematics
ISBN : 0898716594

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This title is a comprehensive treatment of algorithmic, or automatic, differentiation. The second edition covers recent developments in applications and theory, including an elegant NP completeness argument and an introduction to scarcity.

Author : Mykel J. Kochenderfer
Publisher : MIT Press
Page : 521 pages
File Size : 43,54 MB
Release : 2019-03-12
Category : Computers
ISBN : 0262039427

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A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals.

Author : Jörn Steuding
Publisher : Springer
Page : 320 pages
File Size : 50,72 MB
Release : 2007-05-26
Category : Mathematics
ISBN : 3540448225

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These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.

Author : Bart Preneel
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 12,74 MB
Release : 1995-10-25
Category : Computers
ISBN : 9783540605904

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This book contains a set of revised refereed papers selected from the presentations at the Second International Workshop on Fast Software Encryption held in Leuven, Belgium, in December 1994. The 28 papers presented significantly advance the state of the art of software algorithms for two cryptographic primitives requiring very high speeds, namely encryption algorithms and hash functions: this volume contains six proposals for new ciphers as well as new results on the security of the new proposals. In addition, there is an introductory overview by the volume editor. The papers are organized in several sections on stream ciphers and block ciphers; other papers deal with new algorithms and protocols or other recent results.

Author : Rajendra Bhatia
Publisher : SIAM
Page : 200 pages
File Size : 24,6 MB
Release : 2007-07-19
Category : Mathematics
ISBN : 0898716314

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For the SIAM Classics edition, the author has added over 60 pages of material covering recent results and discussing the important advances made in the last two decades. It is an excellent research reference for all those interested in operator theory, linear algebra, and numerical analysis.

Author : Christopher Goodrich
Publisher : Springer
Page : 565 pages
File Size : 12,67 MB
Release : 2016-02-09
Category : Mathematics
ISBN : 3319255622

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This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the subject. Most chapters may be covered or omitted, depending upon the background of the student. For example, the text may be used as a primary reference in an introductory course for difference equations which also includes discrete fractional calculus. Chapters 1—2 provide a basic introduction to the delta calculus including fractional calculus on the set of integers. For courses where students already have background in elementary real analysis, Chapters 1—2 may be covered quickly and readers may then skip to Chapters 6—7 which present some basic results in fractional boundary value problems (FBVPs). Chapters 6—7 in conjunction with some of the current literature listed in the Bibliography can provide a basis for a seminar in the current theory of FBVPs. For a two-semester course, Chapters 1—5 may be covered in depth, providing a very thorough introduction to both the discrete fractional calculus as well as the integer-order calculus.