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Proofs and concepts the fundamenract mathematicstals of abst

This free undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. It is designed to be the textbook for a bridge course that introduces undergraduates to abstract mathematics, but it is also suitable for independent study by undergraduates (or mathematically mature high-school students), or for use as a very inexpensive supplement to undergraduate courses in any field of abstract mathematics.

Pythagorean Theorem History, Applications, and Proofs

More than 2,500 years ago, around 530 BCE, a man by the name of Pythagoras founded a school in modern southeast Italy. Members of the school, which was actually more of a brotherhood, were bound by a pledge of allegiance to their master Pythagoras and took an oath of silence to not divulge secret discoveries. Pythagoreans shared a common belief in the supremacy of numbers, using them to describe and understand everything from music to the physical universe. Studying a wide range of intellectual disciplines, Pythagoreans made a multitude of discoveries, many of which were attributed to Pythagoras himself. No records remain of the actual discoverer, so the identity of the true discoverer may never be known. Perhaps the most famous of the Pythagoreans’ contributions to knowledge is proving what has come to be known as the Pythagorean Theorem.

Avtomatik transmissiyalar: Gidromexanik uzatmalar qo'shaloq ilashmali va variatorli avtomatik transmissiyalar

Kitobda zamonaviy avtomobillarning avtomatik uzatmalar qutilarining uzilishi, konstruksiyasining o'ziga xos tomonlari, ishlash prinsiplari va yuzaga kelishi mumkin bo'lgan nosozliklarni aniqlash yoritilgan. Kitob kasb-hunar kolleji o'quvchilari, haydovchi tayorlovchi avtomaktab talabalariga va o'qituvchi xodimlarga mo'ljallangan bo'lib, undan avlomobil transporti sohasida tahsil olayotgan oliy o'quv yurtlarining talabalari ham foydalanishlari mumkin.

Quaternions and Clifford Geometric Algebras

In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. A feature of quaternions is that multiplication of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space or equivalently as the quotient of two vectors. Quaternions find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations such as in three-dimensional computer graphics, computer vision and crystallographic texture analysis. In practical applications, they can be used alongside other methods, such as Euler angles and rotation matrices, or as an alternative to them, depending on the application.

Real Analysis

This second edition of Real Analysis contains all the material of the first edition originally published by Prentice Hall (Pearson) in 1997, with corrections and revisions and in a new format. For further information on this title and others in the series visit our website. There are pdf files of all of our texts freely available for download as well as instructions on how to order trade paperback copies. In this chapter we provide a review and historical sampling of much of the background needed to embark on a study of the theory of measure, integration, and functional analysis. The setting here is the real line. In later chapters we place most of the theory in an abstract measure space or in a metric space, but the ideas all originate in the situation on the real line. The reader will have a background in elementary analysis, including such ideas as continuity, uniform conti-nuity, convergence, uniform convergence, and sequence limits.

Recent advances in experimental studies of social dilemma games

The articles in this volume collectively represent the latest advances in how people think of social dilemma problems, how we may be able to enhance cooperation and reduce free-riding in such problems and how we can extend the lessons learned to a host of other similar issues facing us. We have learned, for instance, that a "take" frame does not necessarily lead to lower cooperation compared to a "give" frame but combining a "take" frame with fine-grained individual level feedback leads to more extreme behavior in terms of both greater cooperation and greater free-riding. We have also learned that a strategy based on payoff sampling may provide a more parsimonious and less parameter dependent way of modelling behavior in common pool resource extraction games. We find that people behave differently in social dilemmas when making decisions of their own as opposed to deciding on behalf of someone else.

Scaling of Differential Equations. V. 2

The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model.

Теоретические основы информатики

В книге рассматриваются теоретические основы наиболее часто встречающихся информационных процессов: аналого-цифрового преобразования (сканирование), сжатия (архивация), передачи но каналам связи, поиска и аналитико-синтетической обработки информации. Авторы старались найти то общее, что позволяет рассматривать эти проблемы с единой энтропийно-корреляционной точки зрения. Учитывая повышенный интерес к обеспечению секретности передаваемых но каналам связи сообщений с одновременной организацией электронной подписи, авторы рассматривают одну из наиболее перспективных

Теоретические основы электротехники

В книге рассмотрены электрическое и магнитное поля, электрические линейные и нелинейные цепи постоянного и переменного токов, магнитные цепи; излагаются основные методы их расчета; даны примеры расчетов и задачи для закрепления теоретических знаний.

Schwarzschild and Kerr Solutions of Einstein's Field Equation an introduction

Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild(–Droste) solution, and into one specific stationary axially symmetric solution, the Kerr solution. The Schwarzschild solution is unique and its metric can be interpreted as the exterior gravitational field of a spherically symmetric mass. The Kerr solution is only unique if the multipole moments of its mass and its angular momentum take on prescribed values. Its metric can be interpreted as the exterior gravitational field of a suitably rotating mass distribution. Both solutions describe objects exhibiting an event horizon, a frontier of no return. The corresponding notion of a black hole is explained to some extent. Eventually, we present some generalizations of the Kerr solution.

Теория автоматического управления для «ЧАЙНИКОВ»

Эта методичка предназначена для первого знакомства с предметом. Ее задача – объяснить «на пальцах» основные понятия теории автоматического регулирования и сделать так, чтобы после ее прочтения вы смогли воспринимать профессиональную литературу на эту тему. Нужно рассматривать это пособие только как фундамент, стартовую площадку для серьезного изучения серьезного предмета, который может стать очень интересным и увлекательным.

Теория автоматического управления

Теория автоматического управления изучает процессы управления, методы исследования и основы проектирования систем автоматического управления (САУ). Понимая управление каким-либо объектом, как процесс воздействия на него с целью обеспечения требуемого изменения его состояния, под автоматическим управлением будем понимать управление объектом без непосредственного участия человека. В настоящее время теория автоматического управления представляет собой единую научную базу для решения задач управления объектами различной природы: физической, химической, биологической и т.п.

Scientific Computing with MATLAB

The goal of the course is to provide you with skills in scientific computing: tools and techniques that you can use in your own scientific research. We will focus on learning to think about experiments and data in a computational framework, and we will learn to implement specific algorithms using a high-level programming language (MATLAB). Learning how to program will significantly enhance your ability to conduct scientific research today and in the future. Programming skills will provide you with the ability to go beyond what is available in pre-packaged analysis tools, and code your own custom data processing, analysis and visualization pipelines. The course (and these notes) are organized around using MATLAB12, a high-level language and interactive environment for scientific computing.

Теория автоматического управления

Современное машиностроение развивается в условиях жесткой конкуренции и развитие его идет в направлениях: существенное повышение качества продукции; сокращение времени обработки нановых станках за счет технических усовершенствований; повышение интеллектуальной оснащенности машиностроительной отрасли.

Теория автоматического управления

Изложены основы теории управления, включающие общие сведения о системах управления и их моделях, методы анализа и синтеза линейных непрерывных и дискретных систем при детерминированных и стохастических воздействиях, методы анализа нелинейных систем, а также методы оптимизации систем управления. На базе общих принципов системного подхода рассматривается проблематика математического описания систем управления, раскрываются взаимосвязи понятий управления и информации, структуры систем и фундаментальных свойств их поведения - устойчивости, инвариантности и чувствительности.

Scientific Computing

These notes for Scientific Computing is primarily for Math majors and supposes no previous knowledge of numerical analysis or methods. This course consists of both numerical methods and computational physics. The numerical methods content includes standard topics such as IEEE arithmetic, root finding, linear algebra, interpolation and least-squares, integration, differentiation, and differential equations. The physics content includes nonlinear dynamical systems with the pendulum as a model, and computational fluid dynamics with a focus on the steady two-dimensional flow past either a rectangle or a circle.