Mathematics

Algorithmic, or automatic, differentiation (AD) is a growing area of theoretical research and software development concerned with the accurate and efficient evaluation of derivatives for function evaluations given as computer programs. The resulting derivative values are useful for all scientific computations that are based on linear, quadratic, or higher order approximations to nonlinear scalar or vector functions.

AD has been applied in particular to optimization, parameter identification, nonlinear equation solving, the numerical integration of differential equations, and combinations of these. Apart from quantifying sensitivities numerically, AD also yields structural dependence information, such as the sparsity pattern and generic rank of Jacobian matrices. The field opens up an exciting opportunity to develop new algorithms that reflect the true cost of accurate derivatives and to use them for improvements in speed and reliability. 

Product Description:

This book offers a fundamental and practical introduction to the use of computational methods, particularly finite element methods, in the simulation of fluid flows in porous media. It is the first book to cover a wide variety of flows, including single-phase, two-phase, black oil, volatile, compositional, nonisothermal, and chemical compositional flows in both ordinary porous and fractured porous media. In addition, a range of computational methods are used, and benchmark problems of nine comparative solution projects organized by the Society of Petroleum Engineers are presented for the first time in book form. Computational Methods for Multiphase Flows in Porous Media reviews multiphase flow equations and computational methods to introduce basic terminologies and notation. A thorough discussion of practical aspects of the subject is presented in a consistent manner, and the level of treatment is rigorous without being unnecessarily abstract. Each chapter ends with bibliographic information and exercises. This book can be used as a textbook for graduate or advanced undergraduate students in geology, petroleum engineering, and applied mathematics, and as a reference book for professionals in these fields, as well as scientists working in the area of petroleum reservoir simulation. It can also be used as a handbook for employees in the oil industry who need a basic understanding of modeling and computational method concepts and by researchers in hydrology, environmental remediation, and some areas of biological tissue modeling. Calculus, physics, and some acquaintance with partial differential equations and simple matrix algebra are necessary prerequisites.

Primarily designed as a textbook, Trigonometry is a unique treatise on vectors, aiming at providing a fairly complete account of the basic concepts required to build a strong foundation for a student endeavouring to study this subject. The analytical approach to the major theories — Inverse Circular Functions, De-Moivre’s Theorem, Hyperbolic Functions, Gregory’s Series, Trigonometrical Expansions and many more — makes the book highly self-contained and comprehensive guide that succeeds in making the concepts easily understandable.

This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms.

Oxford Handbook of the History of Mathematics (Oxford Handbooks)
Oxford University Press, USA | 2009-02-18 | ISBN: 0199213127 |
800 pages | PDF | 11 MB

This Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practice it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textual sources.

Novel Algorithms and Techniques in Telecommunications and Networking
Springer | 2010-01-29 | ISBN: 904813661X | 489 pages | PDF | 23 MB