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A Textbook of Optics
by Suresh Chandra Mohit Kumar SharmaThis book is designed to serve as a textbook for courses offered to upper-undergraduate students enrolled in physics and explains the broad spectrum of optics in a student-friendly way. The textbook covers the entire syllabi of the undergraduate courses being taught at both national and international universities including adequate details of mathematical expressions to help students understand the subject matter. The topics covered in this book are reflection, refraction, cardinal points, interference, Fresnel diffraction, Fraunhofer diffraction, lasers and holography, fiber optics, etc. This book explains each topic in a simple and lucid language with the help of solved problems. Exercises with multiple choice questions have been given at the end of each chapter for self-assessment. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in senior undergraduate and beginning postgraduate physics students.
A Textbook on Ordinary Differential Equations (UNITEXT #73)
by Shair Ahmad Antonio AmbrosettiThe book is a primer of the theory of Ordinary Differential Equations. Each chapter is completed by a broad set of exercises; the reader will also find a set of solutions of selected exercises. The book contains many interesting examples as well (like the equations for the electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, and many other) which introduce the reader to some interesting aspects of the theory and its applications. The work is mainly addressed to students of Mathematics, Physics, Engineering, Statistics, Computer Sciences, with knowledge of Calculus and Linear Algebra, and contains more advanced topics for further developments, such as Laplace transform; Stability theory and existence of solutions to Boundary Value problems. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available. Instructors who wish to adopt the book may request the manual by writing directly to one of the authors.
A Theoretical Introduction to Numerical Analysis
by Victor S. Ryaben'kii Semyon V. TsynkovA Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study. An access
A Theory of Philosophical Fallacies (Argumentation Library #26)
by Leonard NelsonPresented as a Vorlesung in the German philosophical tradition, this book presents the most detailed account of Nelson's method of argument analysis, celebrated by many luminaries such as Karl Popper. It was written in 1921 in opposition to the relativistic, subjectivistic and nihilistic tendencies of Nelson's time. The book contains an exposition of a method that is a further development of Kant's transcendental dialectics, followed by an application to the critical analysis of arguments by many famous thinkers, including Bentham, Mill, Poincaré, Leibniz, Hegel, Einstein, Bergson, Rickert, Simmel, Brentano, Stammler, Jellinek, Dingler, and Meinong. The book presents a general theory of philosophical argumentation as seen from the viewpoint of the typical fallacies committed by anybody arguing philosophically, whether professional philosophers or philosophical laypeople. Although the nature of philosophy and philosophical argumentation is one of the most recurrent objects of reflection for philosophers, this book represents the first attempt at a general theory of philosophical fallacy. According to Nelson, it is in the shape of false dilemmas that errors in reasoning always emerge, and false dilemmas are always the result of the same mechanism--the unwitting replacement of one concept for another.
A Time Series Approach to Option Pricing: Models, Methods and Empirical Performances
by Florian Ielpo Christophe Chorro Dominique GuéganThe current world financial scene indicates at an intertwined and interdependent relationship between financial market activity and economic health. This book explains how the economic messages delivered by the dynamic evolution of financial asset returns are strongly related to option prices. The Black Scholes framework is introduced and by underlining its shortcomings, an alternative approach is presented that has emerged over the past ten years of academic research, an approach that is much more grounded on a realistic statistical analysis of data rather than on ad hoc tractable continuous time option pricing models. The reader then learns what it takes to understand and implement these option pricing models based on time series analysis in a self-contained way. The discussion covers modeling choices available to the quantitative analyst, as well as the tools to decide upon a particular model based on the historical datasets of financial returns. The reader is then guided into numerical deduction of option prices from these models and illustrations with real examples are used to reflect the accuracy of the approach using datasets of options on equity indices.
A Tiny Handbook of R (SpringerBriefs in Statistics)
by Mike AllerhandThis Brief provides a roadmap for the R language and programming environment with signposts to further resources and documentation.
A Topological Introduction to Nonlinear Analysis
by Robert F. BrownThis third edition is addressed to the mathematician or graduate student of mathematics - or even the well-prepared undergraduate - who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully-expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world. Included in this new edition are several new chapters that present the fixed point index and its applications. The exposition and mathematical content is improved throughout. This book is ideal for self-study for mathematicians and students interested in such areas of geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. It is a sharply focused and highly readable view of nonlinear analysis by a practicing topologist who has seen a clear path to understanding. "For the topology-minded reader, the book indeed has a lot to offer: written in a very personal, eloquent and instructive style it makes one of the highlights of nonlinear analysis accessible to a wide audience. "-Monatshefte fur Mathematik (2006)
A Topology of Mind: Spiral Thought Patterns, the Hyperlinking of Text, Ideas and More (Mathematics in Mind)
by Robert K. Logan Izabella Pruska-OldenhofThis volume covers many diverse topics related in varying degrees to mathematics in mind including the mathematical and topological structures of thought and communication. It examines mathematics in mind from the perspective of the spiral, cyclic and hyperlinked structures of the human mind in terms of its language, its thoughts and its various modes of communication in science, philosophy, literature and the arts including a chapter devoted to the spiral structure of the thought of Marshall McLuhan. In it, the authors examine the topological structures of hypertext, hyperlinking, and hypermedia made possible by the Internet and the hyperlinked structures that existed before its emergence. It also explores the cognitive origins of mathematical thinking of the human mind and its relation to the emergence of spoken language, and studies the emergence of mathematical notation and its impact on education. Topics addressed include:• The historical context of any topic that involves how mathematical thinking emerged, focusing on archaeological and philological evidence. • Connection between math cognition and symbolism, annotation and other semiotic processes. • Interrelationships between mathematical discovery and cultural processes, including technological systems that guide the thrust of cognitive and social evolution. • Whether mathematics is an innate faculty or forged in cultural-historical context• What, if any, structures are shared between mathematics and language
A Tour Through Graph Theory (Textbooks in Mathematics)
by Karin R Saoub<p>A Tour Through Graph Theory introduces graph theory to students who are not mathematics majors. Rather than featuring formal mathematical proofs, the book focuses on explanations and logical reasoning. It also includes thoughtful discussions of historical problems and modern questions. The book inspires readers to learn by working through examples, drawing graphs and exploring concepts. <p>This book distinguishes itself from others covering the same topic. It strikes a balance of focusing on accessible problems for non-mathematical students while providing enough material for a semester-long course.</p>
A Tour of the Calculus
by David BerlinskiIn its largest aspect, the calculus functions as a celestial measuring tape, able to order the infinite expanse of the universe. Time and space are given names, points, and limits; seemingly intractable problems of motion, growth, and form are reduced to answerable questions. Calculus was humanity's first attempt to represent the world and perhaps its greatest meditation on the theme of continuity. Charts and graphs throughout.From the Hardcover edition.
A Tour of the Calculus
by David BerlinskiIn its largest aspect, the calculus functions as a celestial measuring tape, able to order the infinite expanse of the universe. Time and space are given names, points, and limits; seemingly intractable problems of motion, growth, and form are reduced to answerable questions. Calculus was humanity's first attempt to represent the world and perhaps its greatest meditation on the theme of continuity. Charts and graphs throughout.From the Hardcover edition.
A Tour of the Human Body: Amazing Numbers--Fantastic Facts (Number Tours for Curious Kids)
by Jennifer BerneJennifer Berne takes children on a tour of the human body to reveal the wonders of how it works -- with some astonishing numbers and fascinating facts along the way.From our eyes to our toes, kids will find out what makes the human body tick. They&’ll discover that our hearts beat 100,000 times a day, which equals 36 MILLION times a year. And that our tongue&’s 8,000 taste buds can detect only 5 flavors. And that we have 60,000 miles of blood vessels, enough to circle the world more than twice!With such remarkable facts and numbers, and vivid informative illustrations by Dawn DeVries Sokol, this book takes your child on an entertainingly educational journey through the wonders of the human body.
A Trajectory Description of Quantum Processes. II. Applications: A Bohmian Perspective (Lecture Notes in Physics #831)
by Ángel S. Sanz Salvador Miret-ArtésTrajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of "classical" concepts. Beginning as an introductory level suitable for students, this two-volume monograph presents (1) the fundamentals and (2) the applications of the trajectory description of basic quantum processes. This second volume is focussed on simple and basic applications of quantum processes such as interference and diffraction of wave packets, tunneling, diffusion and bound-state and scattering problems. The corresponding analysis is carried out within the Bohmian framework. By stressing its interpretational aspects, the book leads the reader to an alternative and complementary way to better understand the underlying quantum dynamics.
A Transition to Advanced Mathematics (7th Edition)
by Douglas Smith Maurice Eggen Richard St. AndreThe main goal of the book is to improve the student's ability to think and write in a mature mathematical fashion and to provide a solid understanding of the material most useful for advanced courses.
A Transition to Proof: An Introduction to Advanced Mathematics (Textbooks in Mathematics)
by Neil R. NicholsonA Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively. The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof. Features: The text is aimed at transition courses preparing students to take analysis Promotes creativity, intuition, and accuracy in exposition The language of proof is established in the first two chapters, which cover logic and set theory Includes chapters on cardinality and introductory topology
A Trapezoid Is Not a Dinosaur!
by Suzanne MorrisIn this wildly amusing, unconventional shape concept book, Trapezoid is here to declare that he's a shape, too. He's NOT a type of dinosaur!Shape up, shapes! Triangle is hosting auditions for all the best shapes to be in his play. Circle, Square, and Star each get a part. But Trapezoid just doesn't "fit in." Is he even a shape? The others think he sounds like a type of dinosaur. Determined to show off his usefulness, Trapezoid tries to act like the other shapes, to no avail. Eventually, though, Trapezoid celebrates his own distinct shape properties in order to become part of the performance.
A Treatise on Probability
by John Maynard KeynesWith this treatise, an insightful exploration of the probabilistic connection between philosophy and the history of science, John Maynard Keynes (1883-1946) breathed new life into studies of both disciplines. Originally published in 1921, the famous economist's most important mathematical work represented a significant contribution to the theory regarding the logical probability of propositions. Keynes effectively dismantled the classical theory of probability, launching what has since been termed the "logical-relationist" theory. In so doing, he explored the logical relationships between classifying a proposition as "highly probable" and as a "justifiable induction."A Treatise on Probability argues that probability is a matter of logic, which renders it objective: a statement involving probability relations possesses a truth value independent of opinion. Keynes demonstrates that if a hypothesis has even the smallest finite probability, it can be transformed into certainty by a sufficient number of observations. This is his attempt to overcome Humean skepticism by asserting that theoretically grounded hypotheses need only exhibit finite probability to form the basis of science and rational action. Another key idea discussed in A Treatise on Probability is that probability relations constitute only a partially ordered set in the sense that two probabilities cannot necessarily always be compared. Keynes further maintains that probability is a basic concept that cannot be reduced to other concepts.
A Treatise on the Calculus of Finite Differences
by George BooleWritten by a great English mathematician, this classic text begins with the differences of elementary functions and explores interpolation, mechanical quadrature, finite integration, and the summation of series. Several useful tests for the convergence and divergence of series are developed, as is a method for finding the limits of error in series expansions. The latter half of the book discusses difference-equations, including linear, mixed, and partial difference-equations, and concludes with applications to problems in geometry and optics. The text pays particular attention to the connection of the calculus of finite differences with the differential calculus, and more than 200 problems appear in the text (some with solutions). Unabridged republication of the classic 1872 edition.
A Treatise on the Differential Geometry of Curves and Surfaces (Dover Books on Mathematics)
by Luther Pfahler EisenhartCreated especially for graduate students, this introductory treatise on differential geometry has been a highly successful textbook for many years. Its unusually detailed and concrete approach includes a thorough explanation of the geometry of curves and surfaces, concentrating on problems that will be most helpful to students. 1909 edition.
A Triangle for Adaora: An African Book of Shapes
by Ifeoma OnyefuluWhen Adaora's cousin promises to find a triangle for her, he doesn't realize how difficult the task will be. As they search in and around their African village, the cousins encounter all different kinds of shapes, including heart-shaped leaves, round elephant drums, and crescent-shaped plantains. Other books by this author are available in this library.
A Tribe Reborn: How the Cleveland Indians of the ?90s Went from Cellar Dwellers to Playoff Contenders
by Hank Peters George Christian PappasFor almost fifty years, the Cleveland Indians were a joke. They had won the 1948 World Series with one of the greatest teams of all time, but had not been to the playoffs since 1954 (losing to the New York Giants in the World Series). Even the Major League movies poked fun at their inadequacy. That all changed in the 1990s, when the Indians became one of the most dominant teams of the decade.A Tribe Reborn tells the story of a failing franchise, from “The Mistake by the Lake” to “The Curse of Rocky Colavito,” and how a laughingstock team that was on the verge of relocating changed its ways to become a dominant franchise. With the building of the state-of-the-art Jacobs Field (which the Indians sold out a record 455 consecutive games, from 1995–2001) to changes in how their scouting, front office, and locker room were run, the team that nobody cared about became front-page news across the country. With interviews from Jim Thome, Omar Vizquel, Mike Hargrove, John Hart, and many more, A Tribe Reborn is a fantastic look inside how a losing franchise changed its ways to become a perennial powerhouse. While the Indians of the ’90s never won a World Series (appearing twice in 1995 and 1997), they are still remembered for their hard play, amazing talent, and rabid fan base.
A Tribute to the Legend of Professor C. R. Rao: The Centenary Volume (Indian Statistical Institute Series)
by Arijit Chaudhuri Sat N. Gupta Rajkumar RoychoudhuryThis book includes speeches given during five seminar sessions held in honor of Prof. C. R. Rao, on his 100th year. This book also contains a few write-ups touching on the diverse aspects of this august personality. The chapters pay tribute to Prof. C. R. Rao, the Padma Vibhushan awardee, by discussing his life and contributions to the field of statistics. The book also includes a chapter by the Abel Prize winner Prof. S. R. Varadhan who happened to successfully complete his Ph.D. under the guidance of Prof. C. R. Rao.
A Tutorial on the WKB Approximation for Innovative Dirac Materials: Graphene and Beyond (Springer Tracts in Modern Physics #292)
by Andrii IurovThis textbook serves to supplement existing quantum mechanics courses with the WKB (Wentzel–Kramers–Brillouin) theory for recently discovered Dirac materials, such as graphene, a dice lattice, and alpha-T3 materials. This includes finding the semiclassical wave function, coordinate-dependent momentum, semiclassical action, the complete set of transport equations, and applicability conditions for the approximation. The discovery of graphene and its unique electronic behavior has transformed research in condensed matter physics over the last 10-15 years, but core curriculum in standard graduate-level physics courses still does not reflect these new developments and this book intends to close this gap. With a clear focus on various types of Dirac Hamiltonians, the multidimensional theory is only a small part of the book. The derivation of the WKB equations for novel Dirac materials and their applications to electron tunneling, turning points and classically forbidden regions, resonances and localized states, and many other crucial physical problems are methodically presented. This textbook aims to expand the existing approach to presenting the WKB approximation and covers recent developments in its applications. This book also includes many informative graphics, as well as problems and exercises with hints at the end of each chapter. Additional detailed mathematical derivations, as well as code in Mathematica, are added throughout the whole book. Ideal for graduate students and researchers in condensed matter physics, this textbook serves as a modern guide for learning the WKB theory.
A Unified Grand Tour of Theoretical Physics
by Ian D. LawrieA Unified Grand Tour of Theoretical Physics invites its readers to a guided exploration of the theoretical ideas that shape our contemporary understanding of the physical world at the fundamental level. Its central themes, comprising space-time geometry and the general relativistic account of gravity, quantum field theory and the gauge theories of
A Universal Construction for Groups Acting Freely on Real Trees
by Ian Chiswell Thomas MüllerThe theory of R-trees is a well-established and important area of geometric group theory and in this book the authors introduce a construction that provides a new perspective on group actions on R-trees. They construct a group RF(G), equipped with an action on an R-tree, whose elements are certain functions from a compact real interval to the group G. They also study the structure of RF(G), including a detailed description of centralizers of elements and an investigation of its subgroups and quotients. Any group acting freely on an R-tree embeds in RF(G) for some choice of G. Much remains to be done to understand RF(G), and the extensive list of open problems included in an appendix could potentially lead to new methods for investigating group actions on R-trees, particularly free actions. This book will interest all geometric group theorists and model theorists whose research involves R-trees.