65,21 zł

Introduction to Logic Dover Publications Inc.

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PREFACEFROM THE PREFACE TO THE ORIGINAL EDITIONFIRST PART ELEMENTS OF LOGIC. DEDUCTIVE METHODI. ON THE USE OF VARIABLES 1. Constants and variables 2. Expressions containing variables-sentential and designatory functions 3. Formation of sentences by means of variables-universal and existential sentences 4. Universal and existential quantifiers; free and bound variables 5. The importance of variables in mathematics ExercisesII. ON THE SENTENTIAL CALCULUS 6. Logical constants; the old logic and the new logic 7. "Sentential calculus; negation of a sentence, conjunction and disjunction of sentences" 8. Implication or conditional sentence; implication in material meaning 9. The use of implication in mathematics 10. Equivalence of sentences 11. The formulation of definitions and its rules 12. Laws of sentential calculus 13. Symbolism of sentential calculus; truth functions and truth tables 14. Application of laws of sentential calculus in inference 15. "Rules of inference, complete proofs" ExercisesIII. ON THE THEORY OF IDENTITY 16. Logical concepts outside sentential calculus; concept of identity 17. Fundamental laws of the theory of identity 18. Identity of things and identity of their designations; use of quotation marks 19. "Equality in arithmetic and geometry, and its relation to logical identity" 20. Numerical quantifiers ExercisesIV. ON THE THEORY OF CLASSES 21. Classes and their elements 22. Classes and sentential functions with one free variable 23. Universal class and null class 24. Fundamental relations among classes 25. Operations on classes 26. "Equinumerous classes, cardinal number of a class, finite and infinite classes; arithmetic as a part of logic" ExercisesV. ON THE THEORY OF RELATIONS 27. "Relations, their domains and counter-domains; relations and sentential functions with two free variables" 28. Calculus of relations 29. Some properties of relations 30 "Relations which are reflexive, symmetrical and transitive" 31. Ordering relations; examples of other relations 32. One-many relations or functions 33. "One-one relations or biunique functions, and one-to-one correspondences" 34. Many-termed relations; functions of several variables and operations 35. The importance of logic for other sciences ExercisesVI. ON THE DEDUCTIVE METHOD 36. "Fundamental constituents of a deductive theory-primitive and defined terms, axioms and theorems" 37. Model and interpretation of a deductive theory 38. Law of deduction; formal character of deductive sciences 39. Selection of axioms and primitive terms; their independence 40. "Formalization of definitions and proofs, formalized deductive theories" 41. Consistency and completeness of a deductive theory; decision problem 42. The widened conception of the methodology of deductive sciences ExercisesSECOND PART APPLICATIONS OF LOGIC AND METHODOLOGY IN CONSTRUCTING MATHEMATICAL THEORIESVII. CONSTRUCTION OF A MATHEMATICAL THEORY: LAWS OF ORDER FOR NUMBERS 43. Primitive terms of the theory under construction; axioms concerning fundamental relations among numbers 44. Laws of irreflexivity for the fundamental relations; indirect proofs 45. Further theorems on the fundamental relations 46. Other relations among numbers ExercisesVIII. CONSTRUCTION OF A MATHEMATICAL THEORY: LAWS OF ADDITION AND SUBTRACTION 47. "Axioms concerning addition; general properties of operations, concepts of a group and of an Abelian group" 48. Commutative and associative laws for a larger number of summands 49. Laws of monotony for addition and their converses 50. Closed systems of sentences 51. Consequences of the laws of monotony 52. Definition of subtraction; inverse operations 53. Definitions whose definiendum contains the identity sign 54. Theorems on subtraction ExercisesIX. METHODOLOGICAL CONSIDERATIONS ON THE CONSTRUCTED THEORY 55. Elimination of superfluous axioms in the original axiom system 56. Independence of the axioms of the simplified system 57. Elimination of superfluous primitive terms and subsequent simplification of the axiom system; concept of an ordered Abelian group 58. Further simplification of the axiom system; possible transformations of the system of primitive terms 59. Problem of the consistency of the constructed theory 60. Problem of the completeness of the constructed theory ExercisesX. EXTENSION OF THE CONSTRUCTED THEORY. FOUNDATIONS OF ARITHMETIC OF REAL NUMBERS 61. First axiom system for the arithmetic of real numbers 62. Closer characterization of the first axiom system; its methodological advantages and didactical disadvantages 63. Second axiom system for the arithmetic of real numbers 64. Closer characterization of the second axiom system; concepts of a field and of an ordered field 65. Equipollence of the two axiom systems; methodological disadvantages and didactical advantages of the second system ExercisesSUGGESTED READINGSINDEX

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199,37 zł

Trigonometry Birkhauser Boston Inc

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In a sense, trigonometry sits at the center of high school mathematics. It originates in the study of geometry when we investigate the ratios of sides in similar right triangles, or when we look at the relationship between a chord of a circle and its arc. It leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. It also has many applications to physics, astronomy, and other branches of science. It is a very old subject. Many of the geometric results that we now state in trigonometric terms were given a purely geometric exposition by Euclid. Ptolemy, an early astronomer, began to go beyond Euclid, using the geometry of the time to construct what we now call tables of values of trigonometric functions. Trigonometry is an important introduction to calculus, where one stud ies what mathematicians call analytic properties of functions. One of the goals of this book is to prepare you for a course in calculus by directing your attention away from particular values of a function to a study of the function as an object in itself. This way of thinking is useful not just in calculus, but in many mathematical situations. So trigonometry is a part of pre-calculus, and is related to other pre-calculus topics, such as exponential and logarithmic functions, and complex numbers.

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476,64 zł

Engineering Electromagnetics Springer Nature Switzerland AG

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This comprehensive two semester textbook, now in its 4th edition, continues to provide students with a thorough theoretical understanding of electromagnetic field relations while also providing numerous practical applications. The topics follow a tested pattern familiar to the previous edition, each with a brief, introductory chapter followed by a chapter with extensive treatment, 10 to 30 applications, examples and exercises, and problems and summaries. There is new emphasis on problems, examples and applications based on energy harvesting and renewable energy; additional information on sensing and actuation, new material on issues in energy, power, electronics, and measurements, and an emphasis on aspects of electromagnetics relevant to digital electronics and wireless communication. The author adds and revises problems to emphasize the use of tools such as Matlab; new advanced problems for higher level students; a discussion of symbolic and numerical integration; additional examples with each chapter; and new online material including experiments and review questions. The book is an undergraduate textbook at the upper division level, intended for required classes in electromagnetics. It is written in simple terms with all details of derivations included and all steps in solutions listed. It requires little beyond basic calculus and can be used for self-study.Features hundreds of examples and exercises, many new or revised for every topic in the book.Includes over 650 end-of-chapter problems, many of them new or revised, mostly based on applications or simplified applications.Includes a suite of online demonstration software including a computerized Smith Chart.

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275,85 zł

Stochastic Differential Equations Springer-Verlag Berlin and Heidelberg GmbH & Co....

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This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided. Apart from several minor corrections and improvements, based on useful comments from readers and experts, the most important change in the corrected 5th printing of the 6th edition is in Theorem 10.1.9, where the proof of part b has been corrected and rewritten. The corrected 5th printing of the 6th edition is forthcoming and expected in September 2010.

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360,97 zł

Mathematical Analysis I Springer-Verlag Berlin and Heidelberg GmbH & Co....

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This softcover edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, elliptic functions and distributions. Especially notable in this course is the clearly expressed orientation toward the natural sciences and its informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems and fresh applications to areas seldom touched on in real analysis books.§The first volume constitutes a complete course on one-variable calculus along with the multivariable differential calculus elucidated in an up-to-day, clear manner, with a pleasant geometric flavor.

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584,88 zł

Mathematical Problems Springer International Publishing

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The life and soul of any science are its problems. This is particularly true of mathematics, which, not referring to any physical reality, consists only of its problems, their solutions, and, most excitingly, the challenges they pose. Mathematical problems come in many flavours, from simple puzzles to major open problems. The problems stimulate, the stories of their successful solutions inspire, and their applications are wide.The literature abounds with books dedicated to mathematical problems - collections of problems, hints on how to solve them, and even histories of the paths to the solutions of some famous ones. The present book, aimed at the proverbial "bright high-school student", takes a different, more philosophical approach, first dividing mathematical problems into three broad classes - puzzles, exercises, and open problems - and discussing their various roles in one's mathematical education. Various chapters are devoted to discussing examples of each type of problem, along with their solutions and some of the developments arising from them. For the truly dedicated reader, more involved material is offered in an appendix. Mathematics does not exist in a vacuum, whence the author peppers the material with frequent extra-mathematical cultural references. The mathematics itself is elementary, for the most part pre-calculus. The few references to the calculus use the integral notation which the reader need not truly be familiar with, opting to read the integral sign as strange notation for area or as operationally defined by the appropriate buttons on his or her graphing calculator. Nothing further is required. Advance praise for Mathematical Problems "There are many books on mathematical problems, but Smorynski's compelling book offers something unique. Firstly, it includes a fruitful classification and analysis of the nature of mathematical problems. Secondly, and perhaps most importantly, it leads the reader from clear and often amusing accounts of traditional problems to the serious mathematics that grew out of some of them." - John Baldwin, University of Illinois at Chicago "Smorynski manages to discuss the famous puzzles from the past and the new items in various modern theories with the same elegance and personality. He presents and solves puzzles and traditional topics with a laudable sense of humor. Readers of all ages and training will find the book a rich treasure chest." - Dirk van Dalen, Universiteit Utrecht

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294,95 zł

Navier-Stokes Equations Springer International Publishing AG

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This volume is devoted to the study of the Navier-Stokes equations, providing a comprehensive reference for a range of applications: from advanced undergraduate students to engineers and professional mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier-Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier-Stokes equations. § Incompressible Navier-Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior of the fluid, assuming knowledge of its initial and boundary states. These equations are one of the most important models of mathematical physics: although they have been a subject of vivid research for more than 150 years, there are still many open problems due to the nature of nonlinearity present in the equations. The nonlinear convective term present in the equations leads to phenomena such as eddy flows and turbulence. In particular, the question of solution regularity for three-dimensional problem was appointed by Clay Institute as one of the Millennium Problems, the key problems in modern mathematics. The problem remains challenging and fascinating for mathematicians, and the applications of the Navier-Stokes equations range from aerodynamics (drag and lift forces), to the design of watercraft and hydroelectric power plants, to medical applications such as modeling the flow of blood in the circulatory system.

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368,21 zł

Math for Business and Economics Springer-Verlag Berlin and Heidelberg GmbH & Co....

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This textbook contains and explains essential mathematical formulas within an economic context. A broad range of aids and supportive examples will help readers to understand the formulas and their practical applications. This mathematical formulary is presented in a practice-oriented, clear, and understandable manner, as it is needed for meaningful and relevant application in global business, as well as in the academic setting and economic practice. The topics presented include, but are not limited to: mathematical signs and symbols, logic, arithmetic, algebra, linear algebra, combinatorics, financial mathematics, optimisation of linear models, functions, differential calculus, integral calculus, elasticities, economic functions, and the Peren theorem. Given its scope, the book offers an indispensable reference guide and is a must-read for undergraduate and graduate students, as well as managers, scholars, and lecturers in business, politics, and economics.

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122,29 zł

Introduction to Hamiltonian Mechanics Springer Nature Switzerland AG

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This textbook examines the Hamiltonian formulation in classical mechanics with the basic mathematical tools of multivariate calculus. It explores topics like variational symmetries, canonoid transformations, and geometrical optics that are usually omitted from an introductory classical mechanics course. For students with only a basic knowledge of mathematics and physics, this book makes those results accessible through worked-out examples and well-chosen exercises. For readers not familiar with Lagrange equations, the first chapters are devoted to the Lagrangian formalism and its applications. Later sections discuss canonical transformations, the Hamilton-Jacobi equation, and the Liouville Theorem on solutions of the Hamilton-Jacobi equation. Graduate and advanced undergraduate students in physics or mathematics who are interested in mechanics and applied math will benefit from this treatment of analytical mechanics. The text assumes the basics of classical mechanics, as well as linear algebra, differential calculus, elementary differential equations and analytic geometry. Designed for self-study, this book includes detailed examples and exercises with complete solutions, although it can also serve as a class text.

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395,75 zł

Undergraduate Introduction To Financial Mathematics, An (Third Edition) World Scientific Publishing Co Pte Ltd

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This textbook provides an introduction to financial mathematics and financial engineering for undergraduate students who have completed a three- or four-semester sequence of calculus courses. It introduces the theory of interest, discrete and continuous random variables and probability, stochastic processes, linear programming, the Fundamental Theorem of Finance, option pricing, hedging, and portfolio optimization. This third edition expands on the second by including a new chapter on the extensions of the Black-Scholes model of option pricing and a greater number of exercises at the end of each chapter. More background material has been added to the other chapters, allowing the textbook to better stand alone as an introduction to financial mathematics. The reader progresses from a solid grounding in multivariable calculus through a derivation of the Black-Scholes equation, its solution, properties, and applications. The text attempts to be as self-contained as possible without relying on advanced mathematical and statistical topics. The material presented in this book will adequately prepare the reader for graduate-level study in mathematical finance.

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288,42 zł

Political Game Theory Cambridge University Press

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Political Game Theory, first published in 2007, is a self-contained introduction to game theory and its applications to political science. The book presents choice theory, social choice theory, static and dynamic games of complete information, static and dynamic games of incomplete information, repeated games, bargaining theory, mechanism design and a mathematical appendix covering, logic, real analysis, calculus and probability theory. The methods employed have many applications in various disciplines including comparative politics, international relations and American politics. Political Game Theory is tailored to students without extensive backgrounds in mathematics, and traditional economics, however there are also many special sections that present technical material that will appeal to more advanced students. A large number of exercises are also provided to practice the skills and techniques discussed.

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331,93 zł

Introducing General Relativity John Wiley & Sons Inc

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An accessible and engaging introduction to general relativity for undergraduatesIn Introducing General Relativity, the authors deliver a structured introduction to the core concepts and applications of General Relativity. The book leads readers from the basic ideas of relativity--including the Equivalence Principle and curved space-time--to more advanced topics, like Solar System tests and gravitational wave detection. Each chapter contains practice problems designed to engage undergraduate students of mechanics, electrodynamics, and special relativity. A wide range of classical and modern topics are covered in detail, from exploring observational successes and astrophysical implications to explaining many popular principles, like space-time, redshift, black holes, gravitational waves and cosmology. Advanced topic sections introduce the reader to more detailed mathematical approaches and complex ideas, and prepare them for the exploration of more specialized and sophisticated texts.Introducing General Relativity also offers:* Structured outlines to the concepts of General Relativity and a wide variety of its applications* Comprehensive explorations of foundational ideas in General Relativity, including space-time curvature and tensor calculus* Practical discussions of classical and modern topics in relativity, from space-time to redshift, gravity, black holes, and gravitational waves* Optional, in-depth sections covering the mathematical approaches to more advanced ideasPerfect for undergraduate physics students who have studied mechanics, dynamics, and Special Relativity, Introducing General Relativity is an essential resource for those seeking an intermediate level discussion of General Relativity placed between the more qualitative books and graduate-level textbooks.

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1333,58 zł

Mathematical Methods in the Physical Sciences 3e (WSE) John Wiley & Sons Inc

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This book is intended for students who have had a two-semester or three-semester introductory calculus course. Its purpose is to help students develop, in a short time, a basic competence in each of the many areas of mathematics needed in advanced courses in physics, chemistry, and engineering. Students are given sufficient depth to gain a solid foundation (this is not a recipe book). At the same time, they are not overwhelmed with detailed proofs that are more appropriate for students of mathematics. The emphasis is on mathematical methods rather than applications, but students are given some idea of how the methods will be used along with some simple applications.

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185,11 zł

Industrial Robotics Control APress

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Build a complete control system for industrial robots, learning all the theory and practical tips from the perspective of an automation engineer. Explore the details of kinematics, trajectories, and motion control, and then create your own circuit board to drive the electric motors and move the robot.After covering the theory, readers can put what they've learned in practice by programming a control firmware for the robot. Each software component is described in detail, from the HMI and the interpreter of motion commands, to the servo loop controller at the core of each servo drive. In particular, the author presents the commutation algorithm and the servo loop controller for brushless synchronous motors, which are typically employed in robotics applications. Readers will also learn how to calibrate the robot, commission it to the end-user, and design a digital twin to test and monitor the entire workcell in a safe simulated environment.Finally, the book delves into hardware, covering how to select and use electric motors and encoders, how to build servo drives and motion controllers, and how to design your own PCBs. Different electronic components and their application circuits are analyzed, showing the advantages and drawbacks of each. By the end of the book you should be able to design and build electronic boards and write their core firmware to control any kind of industrial robot for all sorts of different practical applications.What you'll learnSolve kinematics models of robotsGenerate safe paths and optimal motion trajectoriesCreate a digital twin of your robot to test and monitor its movementsMaster the electronic commutation and closed-loop control of brushless motorsDesign electronics circuit boards for motion applicationsWho This Book Is For                                             Robotics engineers (and students) who want to understand the theory behind the control of robotics arms, from the kinematic models of their axes to the electronic commutation of their motors. Some basic calculus and linear algebra is required for the understanding of the geometrical framework, while some electronics foundations are helpful to grasp the details of the circuits design.

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297,96 zł

Understanding Probability Cambridge University Press

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Understanding Probability is a unique and stimulating approach to a first course in probability. The first part of the book demystifies probability and uses many wonderful probability applications from everyday life to help the reader develop a feel for probabilities. The second part, covering a wide range of topics, teaches clearly and simply the basics of probability. This fully revised third edition has been packed with even more exercises and examples and it includes new sections on Bayesian inference, Markov chain Monte-Carlo simulation, hitting probabilities in random walks and Brownian motion, and a new chapter on continuous-time Markov chains with applications. Here you will find all the material taught in an introductory probability course. The first part of the book, with its easy-going style, can be read by anybody with a reasonable background in high school mathematics. The second part of the book requires a basic course in calculus.

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t1=0.028, t2=0, t3=0, t4=0.006, t=0.028