Higher Order Derivatives
Higher Order Derivatives

Author: Satya Mukhopadhyay

Publisher: CRC Press

Published: 2012-01-25

Total Pages: 222

ISBN-13: 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.

Communications and Cryptography
Communications and Cryptography

Author: Richard E. Blahut

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 473

ISBN-13: 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.

Evaluating Derivatives
Evaluating Derivatives

Author: Andreas Griewank

Publisher: SIAM

Published: 2008-11-06

Total Pages: 448

ISBN-13: 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.

APEX Calculus
APEX Calculus

Author: Gregory Hartman

Publisher:

Published: 2015

Total Pages: 0

ISBN-13: 9781514225158

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APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).

Perturbation Bounds for Matrix Eigenvalues
Perturbation Bounds for Matrix Eigenvalues

Author: Rajendra Bhatia

Publisher: SIAM

Published: 2007-07-19

Total Pages: 200

ISBN-13: 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.

Active Calculus 2018
Active Calculus 2018

Author: Matthew Boelkins

Publisher: Createspace Independent Publishing Platform

Published: 2018-08-13

Total Pages: 560

ISBN-13: 9781724458322

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Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface.

Value-Distribution of L-Functions
Value-Distribution of L-Functions

Author: Jörn Steuding

Publisher: Springer

Published: 2007-05-26

Total Pages: 320

ISBN-13: 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.

Derivatives and Integrals of Multivariable Functions
Derivatives and Integrals of Multivariable Functions

Author: Alberto Guzman

Publisher: Springer Science & Business Media

Published: 2003-08-22

Total Pages: 346

ISBN-13: 9780817642747

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This work provides a systematic examination of derivatives and integrals of multivariable functions. The approach taken here is similar to that of the author’s previous text, "Continuous Functions of Vector Variables": specifically, elementary results from single-variable calculus are extended to functions in several-variable Euclidean space. Topics encompass differentiability, partial derivatives, directional derivatives and the gradient; curves, surfaces, and vector fields; the inverse and implicit function theorems; integrability and properties of integrals; and the theorems of Fubini, Stokes, and Gauss. Prerequisites include background in linear algebra, one-variable calculus, and some acquaintance with continuous functions and the topology of the real line. Written in a definition-theorem-proof format, the book is replete with historical comments, questions, and discussions about strategy, difficulties, and alternate paths. "Derivatives and Integrals of Multivariable Functions" is a rigorous introduction to multivariable calculus that will help students build a foundation for further explorations in analysis and differential geometry.