Mathematics

by Serge Preston , Language: English

This text presents and studies the method of so –called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations.

by M S Burgin , Language: English

Neoclassical analysis extends methods of classical calculus to reflect uncertainties that arise in computations and measurements. In it, ordinary structures of analysis, that is, functions, sequences, series, and operators, are studied by means of fuzzy concepts: fuzzy limits, fuzzy continuity, and fuzzy derivatives. For example, continuous functions, which are studied in the classical analysis, become a part of the set of the fuzzy continuous functions studied in neoclassical analysis. Aiming at representation of uncertainties and imprecision and extending the scope of the classical calculus and analysis, neoclassical analysis makes, at the same time, methods of the classical calculus more precise with respect to real life applications.

by Frank W J Olver , National Institute of Standards and Technology , Language: English

Modern developments in theoretical and applied science depend on knowledge of the properties of mathematical functions, from elementary trigonometric functions to the multitude of special functions. These functions appear whenever natural phenomena are studied, engineering problems are formulated, and numerical simulations are performed. They also crop up in statistics, financial models, and economic analysis. Using them effectively requires practitioners to have ready access to a reliable collection of their properties.

by Gelya Frank , Language: English

This remarkable book – by turns moving, funny, and revelatory – records the relationship that developed between the women over the next twenty years. An empathic listener and participant in DeVries’ life, and a scholar of the feminist and disability rights movements, Frank argues that Diane DeVries is a perfect example of an American woman coming of age in the second half of the twentieth century.

by Joseph Schmuller , Language: English

Learn all of Excel’s statistical toolsTest your hypotheses and draw conclusionsUse Excel to give meaning to your dataUse Excel to interpret statsStatistical analysis with Excel is incredibly useful—and this book shows you that it can be easy, too! You’ll discover how to use Excel’s perfectly designed tools to analyze and understand data, predict trends, make decisions, and more. Tackle the technical aspects of Excel and start using them to interpret your data!Inside…Covers Excel 2016 for Windows® & Mac® usersCheck out new Excel stuffMake sense of worksheetsCreate shortcutsTool around with analysisUse Quick StatisticsGraph your dataWork with probabilityHandle random variables

by Leon O Chua , Language: English

Volume IV continues the author’s odyssey on l-D cellular automata as chronicled in Volumes I, II and III, by uncovering a novel quasi-ergodicity phenomenon involving orbits meandering among omega-limit orbits of complex (group 5) and hyper (group 6) Bernoulli rules. This discovery is embellished with analytical formulas characterizing the fractal properties of characteristic functions, as well as explicit formulas for generating colorful and pedagogically revealing isomorphic basin tree diagrams.

by Hong-Mo Chan , Language: English

The book introduces Chinese culture to readers of English, using poetry from the various periods rendered into English verse to bring back to life past Chinese society as it developed from about 1000 B.C to the form we see today. With China’s increasing importance on the world stage today, many readers, no doubt, would want to learn more about its ancient culture. However, to learn about a culture from its history alone, especially one as long as that of China, is time-consuming and requires a historian’s expert skill.

by K Ramachandra , Language: English

"Theory of Numbers: A Textbook" is aimed at students of Mathematics who are graduates or even undergraduates. Very little prerequisites are needed. The reader is expected to know the theory of functions of a real variable and in some chapters complex integration and some simple principles of complex function theory are assumed. The entire book is self contained except theorems 7 and 9 of chapter 11 which are assumed. The most ambitious chapter is chapter 11 where the most attractive result on difference between consecutive primes is proved.

by Mary Jane Sterling , Language: English

Factor fearlessly, conquer the quadratic formula, and solve linear equationsThere’s no doubt that algebra can be easy to some while extremely challenging to others. If you’re vexed by variables, Algebra I For Dummies, 2nd Edition provides the plain-English, easy-to-follow guidance you need to get the right solution every time!Now with 25% new and revised content, this easy-to-understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems with confidence.

by Mark Zegarelli , Language: English

Tips for simplifying tricky basic math and pre-algebra operationsWhether you’re a student preparing to take algebra or a parent who wants or needs to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you’ll build necessary math skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations.Explanations and practical examples that mirror today’s teaching methodsRelevant cultural vernacular and referencesStandard For Dummiesmaterials that match the current standard and designBasic Math & Pre-Algebra For Dummies takes the intimidation out of tricky operations and helps you get ready for algebra!

by David Borthwick , Language: English

Authors: Borthwick, DavidProvides an accessible introduction to geometric scattering theory and the theory of resonancesDiscusses important developments such as resonance counting, analysis of the Selberg zeta function, and the Poisson formula New chapters cover resolvent estimates, wave propagation, and Naud’s proof of a spectral gap for convex hyperbolic surfacesMakes use of new techniques for resonance plotting that more clearly illustrate existing results of resonance distributionThis text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field.

by Ferrante Neri , Language: English

Authors: Neri, FerranteCovers all aspects of linear algebra from the perspective of computational science and engineeringProvides both a technical approach and an informal interpretation of mathematicsIncludes examples with definitions and theoremsPresents a chapter where the study of an electrical network is shown as an algebraic exerciseThis book presents the main concepts of linear algebra from the viewpoint of applied scientists such as computer scientists and engineers, without compromising on mathematical rigor.

by Paolo Biscari , Language: Italian

Il libro mira a fornire le basi di Meccanica Razionale, corredando l’esposizione teorica con un alto numero di esempi ed esercizi, di tutti i quali si fornisce la soluzione. Il testo è particolarmente indicato per i corsi di breve o media durata, e può servire da appoggio a corsi che si sviluppino al secondo, o anche al primo anno del corso di studi universitario.

by D Somasundaram , Language: English

Differential Geometry: A First Course is an introduction to the classical theory of space curves and surfaces offered at the Graduate and Post- Graduate courses in Mathematics. Based on Serret-Frenet formulae, the theory of space curves is developed and concluded with a detailed discussion on fundamental existence theorem. The theory of surfaces includes the first fundamental form with local intrinsic properties, geodesics on surfaces, the second fundamental form with local non-intrinsic properties and the fundamental equations of the surface theory with several applications.

by D Somasundaram , Language: English

Though ordinary differential equations is taught as a core course to students in mathematics and applied mathematics, detailed coverage of the topics with sufficient examples is unique.Written by a mathematics professor and intended as a textbook for third- and fourth-year undergraduates, the five chapters of this publication give a precise account of higher order differential equations, power series solutions, special functions, existence and uniqueness of solutions, and systems of linear equations.R

by O E Barndorff-Nielsen , W S Kendall , M N M Van Lieshout , Language: English

Stochastic geometry involves the study of random geometric structures, and blends geometric, probabilistic, and statistical methods to provide powerful techniques for modeling and analysis. Recent developments in computational statistical analysis, particularly Markov chain Monte Carlo, have enormously extended the range of feasible applications. Stochastic Geometry: Likelihood and Computation provides a coordinated collection of chapters on important aspects of the rapidly developing field of stochastic geometry, including:o a "crash-course" introduction to key stochastic geometry themeso considerations of geometric sampling bias issueso tesselationso shapeo random setso image analysiso spectacular advances in likelihood-based inference now available to stochastic geometry through the techniques of Markov chain Monte Carlo

by Mark Ryan , Language: English

Slay the calculus monster with this user-friendly guideCalculus For Dummies, 2nd Edition makes calculus manageable—even if you’re one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English instead of math-speak.

by Robert C Wrede , Language: English

This broad introduction to vector and tensor analysis is designed for the advanced undergraduate or graduate student in mathematics, physics, and engineering as well as for the practicing engineer or physicist who needs a theoretical understanding of these essential mathematical tools. In recent years, the vector approach has found its way even into writings on aspects of biology, economics, and other sciences.The many and various topics covered include: the algebra of vectors — linear dependence and independence, transformation equations, the inner product, the cross product, and the algebra of matrixes; the differentiation of vectors — geometry of space curves, kinematics, moving frames of reference, Newtonian orbits and special relativity theory; partial differentiation of vectors — geometry of space curves, kinematics, moving frames of reference, Newtonian orbits and special relativity theory; partial differentiation and associated concepts — surface representations, bases in general coordinate systems, and maxima and minima of functions of two variables; the integration of vectors — line integrals, surface integrals, surface tensors and volume integrals; tensor algebra and analysis — fundamental notions of n-space, transformations and tensors, Riemannian geometry, tensor processes of differentiation, geodesics, the curvature tensor and its algebraic properties, and general relativity theory.T

by Sorin Dragomir , Mohammad Hasan Shahid , Falleh R Al-Solamy , Language: English

This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential Cauchy–Riemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds.I

by David C Lay , Language: English

Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students’ understanding of these concepts is vital to their mastery of the subject.

by H Kisilevsky , Maruti Ram Murty , Language: English

This book represents the proceedings of a workshop on elliptic curves held in St. Adele, Quebec, in February 1992. Containing both expository and research articles on the theory of elliptic curves, this collection covers a range of topics, from Langlands’s theory to the algebraic geometry of elliptic curves, from Iwasawa theory to computational aspects of elliptic curves. This book is especially significant in that it covers topics comprising the main ingredients in Andrew Wiles’s recent result on Fermat’s Last Theorem.

by Steven G Krantz , Language: English

A Guide to Real Variables is an aid and conceptual support for students taking an undergraduate course on real analysis. It focuses on concepts, results, examples and illustrative figures, rather than the details of proofs, in order to remain a concise guide which students can dip into. The core topics of a first real analysis course are covered, including sequences, series, modes of convergence, the derivative, the integral and metric spaces. The next book in this series, Folland’s A Guide to Advanced Real Analysis is designed to naturally follow on from this book, and introduce students to graduate level real analysis.

by Joram Lindenstrauss , Lior Tzafriri , Language: English

From the reviews: . . . the book is written in the best tradition of the beautiful series in which it appears. The material it presents is hard to find in other books. For people working in the structure theory of Banach spaces it will be most valuable as a source of references and inspiration.

by Paul Teetor , Language: English

R is a powerful tool for statistics and graphics, but getting started with this language can be frustrating. This short, concise book provides beginners with a selection of how-to recipes to solve simple problems with R. Each solution gives you just what you need to know to use R for basic statistics, graphics, and regression.