كتب رياضيات mathmatic

Siegfried Flügge, "Practical Quantum Mechanics"
Springer (December 17, 1998) | ISBN:3540650350 | 624 pages | Djvu | 2,6 Mb


Review
From the reviews: "Anyone who has taught a course of quantum mechanics knows the difficulty of providing practical examples which are within the mathematical competence of the students and can be completed in a reasonable time. In this book will be found 219 problems, together with their solutions, which will greatly extend the repertoire. (...) The first volume deals exclusively with one-body problems without spin. (...) In the second volume the problems cover a wider range and include illustrations of the introduction of spin, the interactions between two and three particles, quantum statistics and the Dirac relativistic equation with shorter sections on non-stationary problems and radiation theory. (...)" Nature, Sept. 10, 1971. "The student who can master these problems will have a good grasp of the practical applications of quantum theory and, therefore, of the basic concepts as well. I recommend the book unreservedly." The Australian Physicist,

S. Andersson (Editor), K. Larsson (Editor), M. Larsson (Editor), M. Jacob (Editor), "Biomathematics"
Elsevier Science | ISBN: 0444502734 | 1st edition (October 1, 1999) | PDF | 534 pages | 45181 KB


This book presents new mathematics for the description of structure and dynamics in molecular and cellular biology. On an exponential scale it is possible to combine functions describing inner organisation, including finite periodicity, with functions for outside morphology into a complete definition of structure. This mathematics is particularly fruitful to apply at molecular and atomic distances. The structure descriptions can then be related to atomic and molecular forces and provide information on structural mechanisms. The calculations have been focussed on lipid membranes forming the surface layers of cell organelles. Calculated surfaces represent the mid-surface of the lipid bilayer. Membrane dynamics such as vesicle transport are described in this new language. Periodic membrane assemblies exhibit conformations based on the standing wave oscillations of the bilayer, considered to reflect the true dynamic nature of periodic membrane structures. As an illustration the structure of an endoplasmatic reticulum has been calculated. The transformation of such cell membrane assemblies into cubosomes seems to reflect a transition into vegetative states. The organisation of the lipid bilayer of nerve cells is analyzed, taking into account an earlier observed lipid bilayer phase transition associated with the depolarisation of the membrane. Evidence is given for a new structure of the alveolar surface, relating the mathematical surface defining the bilayer organisation to new experimental data. The surface layer is proposed to consist of a coherent phase, consisting of a lipid-protein bilayer curved according to a classical surface - the CLP surface. Without employing this new mathematics it would not be possible to give an analytical description of this structure and its deformation during the respiration cycle. In more general terms this mathematics is applied to the description of the structure and dynamic properties of motor proteins, cytoskeleton proteins, and RNA/DNA. On a macroscopic scale the motions of cilia, sperm and flagella are modelled.

This mathematical description of biological structure and dynamics, biomathematics, also provides significant new information in order to understand the mechanisms governing shape of living organisms.

Fokko Jan Dijksterhuis, "Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century"
Springer | ISBN: 1402026978 | 1 edition (November 3, 2004) | PDF | 289 pages | 3026 KB


In 1690, Christiaan Huygens (1629-1695) published Traité de la Lumière, containing his renowned wave theory of light. It is considered a landmark in seventeenth-century science, for the way Huygens mathematized the corpuscular nature of light and his probabilistic conception of natural knowledge. This book discusses the development of Huygens' wave theory, reconstructing the winding road that eventually led to Traité de la Lumière. For the first time, the full range of manuscript sources is taken into account. In addition, the development of Huygens' thinking on the nature of light is put in the context of his optics as a whole, which was dominated by his lifelong pursuit of theoretical and practical dioptrics. In so doing, this book offers the first account of the development of Huygens' mathematical analysis of lenses and telescopes and its significance for the origin of the wave theory of light. As Huygens applied his mathematical proficiency to practical issues pertaining to telescopes including trying to design a perfect telescope by means of mathematical theory his dioptrics is significant for our understanding of seventeenth-century relations between theory and practice. With this full account of Huygens' optics, this book sheds new light on the history of seventeenth-century optics and the rise of the new mathematical sciences, as well as Huygens' oeuvre as a whole. Students of the history of optics, of early mathematical physics, and the Scientific Revolution, will find this book enlightening.

Julius B. Barbanel, "The Geometry of Efficient Fair Division"
Cambridge University Press | ISBN: 0521842484 | January 24, 2005 | PDF | 472 pages | 2360 KB

What is the best way to divide a cake and allocate the pieces among some finite collection of players? In this book, the cake is a measure space, and each player uses a countably additive, non-atomic probability measure to evaluate the size of the pieces of cake, with different players generally using different measures. The author investigates efficiency properties (is there another partition that would make everyone at least as happy, and would make at least one player happier, than the present partition?) and fairness properties (do all players think that their piece is at least as large as every other player's piece?). He focuses exclusively on abstract existence results rather than algorithms, and on the geometric objects that arise naturally in this context. By examining the shape of these objects and the relationship between them, he demonstrates results concerning the existence of efficient and fair partitions.

Brian P. Cleary, "How Long or How Wide?: A Measuring Guide (Math Is Categorical)"
Millbrook Press | ISBN 082256694X | 2007-07-11 | 32 Pages | Rar'd PDF | 4.8 Mb

This small ebook is intended to teach the children how to measure length, width and height.

Y. Nesterov “Introductory Lectures on Convex Optimization: A Basic Course"
Springer | 2003-12-31 | ISBN:1402075537 | Djvu | 254 pages | 5,3 Mb


This is the first elementary exposition of the main ideas of complexity theory for convex optimization. Up to now, most of the material can be found only in special journals and research monographs. The book covers optimal methods and lower complexity bounds for smooth and non-smooth convex optimization. A separate chapter is devoted to polynomial-time interior-point methods.
Audience: The book is suitable for industrial engineers and economists.

Kosta DoSen, Zoran Petrić “Proof-Net Categories"
Polimetrica, International Scientific Publisher | 2007-12-11 | ISBN:8876990801 | PDF | 156 pages | 1 Mb


Star-autonomous categories are a brand of symmetric monoidal closed categories of particular interest for classical linear logic. This work formulates equationally a precise notion of star-autonomous category without unit objects, which is called proof-net category. A coherence theorem analogous to the coherence theorem for symmetric monoidal closed categories with respect to graphs is proved for proof-net categories. It is also proved that the free proof-net category generated by a set of objects is isomorphic to a full subcategory of the free star-autonomous category generated by the same set of objects. This yields a very useful coherence theorem for star-autonomous categories involving the unit objects, exactly analogous to the coherence theorem for symmetric monoidal closed categories. An analogous coherence result is proved also for proof-net categories with the mix principle of linear logic. The graphs involved in these coherence theorems are the relevant portions of proof nets that one needs to solve the question whether a diagram of arrows commutes. Proofs are inspired by methods of proof theory. The results of this work are of interest for general proof theory. They show how generality of proofs provides a criterion for identity of proofs in a fragment of linear logic. They also make a contribution to the study of coherence in symmetric monoidal closed categories.

Wolfram Pohlers, Pohlers " Proof Theory: An Introduction"
Springer | 2002-05-02 | ISBN: 3540518428 | PDF | 213 pages | 9 Mb

Although this is an introductory text on proof theory, most of its contents is not found in a unified form elsewhere in the literature, except at a very advanced level. The heart of the book is the ordinal analysis of axiom systems, with particular emphasis on that of the impredicative theory of elementary inductive definitions on the natural numbers. The "constructive" consequences of ordinal analysis are sketched out in the epilogue. The book provides a self-contained treatment assuming no prior knowledge of proof theory and almost none of logic. The author has, moreover, endeavoured not to use the "cabal language" of proof theory, but only a language familiar to most readers.

Jean-Luc Lebrun " Scientific Writing: A Reader and Writer's Guide"
World Scientific Publishing Company; 1 edition (April 6, 2007) | ISBN:9812704736 | PDF | 224 pages | 1,5 Mb



Don Norman, Professor, Northwestern University, USA
... this book, and Lebrun's wisdom, is so essential, so correct, and so badly needed.

Description
Given that scientific material can be hard to comprehend, sustained attention and memory retention become major reader challenges. Scientific writers must not only present their science, but also work hard to generate and sustain the interest of readers. Attention-getters, sentence progression, expectation-setting, and memory offloaders are essential devices to keep readers and reviewers engaged. The writer needs to have a clear understanding of the role played by each part of a paper, from its eye-catching title to its eye-opening conclusion. This book walks through the main parts of a paper; that is, those parts which create the critical first impression. The unique approach in this book is its focus on the reader rather than the writer. Senior scientists who supervise staff and postgraduates can use the book to review drafts and to help with the writing as well as the science. Young researchers can find solid guidelines that reduce the confusion all new writers face. Published scientists can finally move from what feels right to what is right, identifying mistakes they thought were acceptable, and fully appreciating their responsibility: to guide the reader along carefully laid-out reading tracks.

Diagram Group “Measurements & Conversions: A Complete Guide "
Running Press Book Publishers | 1994-09 | ISBN:1561384666 | PDF | 254 pages | 3,7 Mb

Provides a theoretical foundation as well as practical tools for the analysis of multivariate data, using case studies and MINITAB computer macros to illustrate basic and advanced quality control methods. This work offers an approach to quality control that relies on statistical tolerance regions, and discusses computer graphic analysis highlighting multivariate profile charts.

Edward A. Bender, S. Gill Williamson “Foundations of Combinatorics with Applications"
Dover Publications | 2006-02-06 | ISBN:0486446034 | PDF | 480 pages | 3,9 Mb

This introduction to combinatorics is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. Covers basic counting, functions, decision trees, and sieving methods; fundamental concepts in graph theory and a sampler of graph topics; induction and recursion, sorting theory, and rooted plane trees. Numerous exercises (some with solutions), notes, and references. Includes 75 figures. Appendixes.

Edward A. Bender, S. Gill Williamson “Mathematics for Algorithm and Systems Analysis"
Dover Publications | 2005-07-27 | ISBN:0486442500 | PDF | 256 pages | 1,7 Mb


Discrete mathematics is fundamental to computer science, and this up-to-date text assists undergraduates in mastering the ideas and mathematical language to address problems that arise in the field's many applications. It consists of 4 units of study: counting and listing, functions, decision trees and recursion, and basic concepts of graph theory.

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V.M.A. Leitao, C.J.S. Alves, C. Armando Duarte “Advances in Meshfree Techniques"
Springer | 2007-05-18 | ISBN:1402060947 | PDF | 322 pages | 3,2 Mb

In recent years meshless/meshfree methods have gained a considerable attention in engineering and applied mathematics. The variety of problems that are now being addressed by these techniques continues to expand and the quality of the results obtained demonstrates the effectiveness of many of the methods currently available. The book presents a significant sample of the state of the art in the field with methods that have reached a certain level of maturity while also addressing many open issues.

The book collects extended original contributions presented at the first ECCOMAS Conference on Meshless Methods held in 2005 in Lisbon. The list of contributors reveals a mix of highly distinguished authors as well as quite young but very active and promising researchers, thus giving the reader an interesting and updated view of different mesh reduction methods and its range of applications. The material presented is appropriate for researchers, engineers, physicists, applied mathematicians and graduate students interested in this active research area.

Robert Watts “Essentials of Applied Mathematics for Scientists and Engineers"
Morgan and Claypool Publishers | ISBN: 1598291866 | PDF | 180 pages | 1,3 Mb

This is a book about linear partial differential equations that are common in engineering and the physical sciences. It will be useful to graduate students and advanced undergraduates in all engineering fields as well as students of physics, chemistry, geophysics and other physical sciences and professional engineers who wish to learn about how advanced mathematics can be used in their professions. The reader will learn about applications to heat transfer, fluid flow, and mechanical vibrations. The book is written in such a way that solution methods and application to physical problems are emphasized. There are many examples presented in detail and fully explained in their relation to the real world. References to suggested further reading are included. The topics that are covered include classical separation of variables and orthogonal functions, Laplace transforms, complex variables, and Sturm-Liouville transforms.

V.D. Milman, G. Schechtman “Geometric Aspects of Functional Analysis: Israel Seminar 1996-2000"
Springer | 2000-11-27 | ISBN:3540410708 | Djvu | 287 pages | 1,7 Mb

This volume of original research papers from the Israeli GAFA seminar during the years 1996-2000 not only reports on more traditional directions of Geometric Functional Analysis, but also reflects on some of the recent new trends in Banach Space Theory and related topics. These include the tighter connection with convexity and the resulting added emphasis on convex bodies that are not necessarily centrally symmetric, and the treatment of bodies which have only very weak convex-like structure. Another topic represented here is the use of new probabilistic tools; in particular transportation of measure methods and new inequalities emerging from Poincaré-like inequalities.

Pietro Aiena “Fredholm and Local Spectral Theory, with Applications to Multipliers"
Springer | 2004-02-29 | ISBN:1402018304 | PDF | 444 pages | 3,3 Mb

This book shows the deep interaction between two important theories: Fredholm and local spectral theory. A particular emphasis is placed on the applications to multipliers and in particular to convolution operators. The book also presents some important progress, made in recent years, in the study of perturbation theory for classes of operators which occur in Fredholm theory.

Numerical Computing with Matlab
Society for Industrial Mathematics | 2004-01-01 | ISBN: 0898715601 | 348 pages | PDF | 3,5 MB

The book makes extensive use of computer graphics, including interactive graphical expositions of numerical algorithms. It provides more than 70 M-files, which can be downloaded from the text Web site www.mathworks.com/moler. Many of the numerous exercises involve modifying and extending these programs. The topics covered include an introduction to MATLAB; linear equations; interpolation; zeros and roots; least squares; quadrature; ordinary differential equations; Fourier analysis; random numbers; eigenvalues and singular values; and partial differential equations. Motivating applications include modern problems from cryptography, touch-tone dialing, Google page-ranking, atmospheric science and image processing, as well as classical problems from physics and engineering.

Advanced Engineering Mathematics
John Wiley & Sons | 2005-12-29 | ISBN: 0471728977 | 1232 pages | Djvu | 31,5 MB

This is an absolutely great book. At over 1000 pages it's a real opus - covering everything from ordinary differential equations, linear algebra, vector calculus, fourier analysis, complex analysis and probability. It's exceptionally well written - with plenty of clear examples, diagrams and exercises - constantly cross referencing back to the particular idea or formula that an example is employing. It presupposes only elementary calculus - and so makes an excellent university textbook to accompany study, or as a self-study book to further your maths knowledge.