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This unique monograph by a noted UCLA professor examines in detail the mathematics of Kerr black holes, which possess the properties of mass and angular momentum but carry no electrical charge. Suitable for advanced undergraduates and graduate students of mathematics, physics, and astronomy as well as professional physicists, the self-contained treatment constitutes an introduction to modern techniques in differential geometry. The text begins with a substantial chapter offering background on the mathematics needed for the rest of the book. Subsequent chapters emphasize physical interpretations of geometric properties such as curvature, geodesics, isometries, totally geodesic submanifolds, and topological structure. Further investigations cover relativistic concepts such as causality, Petrov types, optical scalars, and the Goldberg-Sachs theorem. Four helpful appendixes supplement the text.

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As Applied to Gamma, Beta, Legendre and Bessel Functions

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Nearly 200 problems, each with a detailed, worked-out solution, deal with the properties and applications of the gamma and beta functions, Legendre polynomials, and Bessel functions. The first two chapters examine gamma and beta functions, including applications to certain geometrical and physical problems such as heat-flow in a straight wire. The following two chapters treat Legendre polynomials, addressing applications to specific series expansions, steady-state heat-flow temperature distribution, gravitational potential of a circular lamina, and application of Gauss's mechanical quadrature formula with pertinent table. The final chapters explore Bessel functions, discussing differentiation formulas, generating functions, relations to Legendre polynomials, and other applications.This volume constitutes a useful tool for professional engineers and experimental physicists. Students of mathematics, physics, and engineering will particularly benefit from the book's expanded solutions.

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Anatomy, Perspective and Composition for the Artist

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Splendid color illustrations by a distinguished painter and teacher highlight this volume of practical instruction in the foundations of art. Perfect for intermediate-level and advanced artists wishing to take their work to the next level, this manual combines detailed anatomy studies with guidance in the principles and practice of perspective and the art of composition.Author Stan Smith interprets the traditions of European art from the Renaissance onward, providing step-by-step diagrams that develop students' understanding and familiarity with concepts and techniques. Technical and expressive qualities receive equal emphasis. In addition to its value as a source of instruction, this book also functions as an essential reference.

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Thermodynamics of Small Systems, Parts I & II

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This authoritative summary of the basics of small system, or nonmacroscopic, thermodynamics was written by the field's founder. Originally published in two volumes, the text remains essential reading in an area in which the practical aim is to derive equations that provide interconnections among various thermodynamic functions.Part I introduces the basics of small system thermodynamics, exploring environmental variables, noting throughout the ways in which small thermodynamic systems differ operationally from macroscopic systems. Part II explores binding on macromolecules and aggregation, completes the discussion of environmental variables, and includes brief summaries of certain special topics, including electric and magnetic fields, spherical drops and bubbles, and polydisperse systems.

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Principle of Aeroelasticity constitutes an attempt to bring order to a group of problems which have coalesced into a distinct and mature subdivision of flight-vehicle engineering. The authors have formulated a unifying philosophy of the field based on the equations of forced motion of the elastic flight vehicle. A distinction is made between static and dynamic phenomena, and beyond this the primary classification is by the number of independent space variables required to define the physical system. Following an introductory chapter on the field of aeroelasticity and its literature, the book continues in two major parts. Chapters 2 through 5 give general methods of constructing static and dynamic equations and deal specifically with the laws of mechanics for heated elastic solids, forms of aerodynamic operators, and structural operators. Chapters 6 through 10 survey the state of aeroelastic theory. The chapters proceed from simplified cases which have only a small, finite number of degrees of freedom, to one-dimensional systems (line structures), and finally to two-dimensional systems (plate- and shell-like structures). Chapter 9 combines some of the previous results by treating the unrestrained elastic vehicle in flight. All these chapters assume linear systems with properties independent of time, but Chapter 10 takes up the subject of systems which must be represented by nonlinear equations or by equations with time-varying coefficients.

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One of the best books on a relatively new branch of mathematics, this text is the work of a leading authority in the field of topos theory. Suitable for advanced undergraduates and graduate students of mathematics, the treatment focuses on how topos theory integrates geometric and logical ideas into the foundations of mathematics and theoretical computer science.After a brief overview, the approach begins with elementary toposes and advances to internal category theory, topologies and sheaves, geometric morphisms, and logical aspects of topos theory. Additional topics include natural number objects, theorems of Deligne and Barr, cohomology, and set theory. Each chapter concludes with a series of exercises, and an appendix and indexes supplement the text.

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"In America, everything was possible," recalls Louis Adamic of Slovenia. "There even the common people were 'citizens,' not 'subjects' . . . a citizen, or even a non-citizen foreigner, could walk up to the President of the United States and pump his hand. Indeed, that seemed to be a custom in America."The history and experience of immigration remain central to American culture, past and present. This anthology surveys the recollections of emigrants from around the world who sought new lives in the United States. Their stories range in mood and setting from the misery of an Englishman in colonial Virginia, bound by indentured servitude, to the cultural commentary of an Iranian woman in California. Poignant, eye-opening reflections include those of a Polish sweatshop laborer, a Chinese businessman, an Italian bootblack, and a Ukrainian musician, in addition to observations and reminiscences by Jacob Riis, Edwidge Danticat, Junot Diaz, and other well-known authors.

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When Gerda's beloved playmate, Kai, disappears one winter afternoon, all of the grownups give him up as forever lost. But Gerda knows in her heart that Kai can be rescued, and with nothing more than the clothes on her back, she journeys to a far country, populated by an ancient sorceress, friendly crows, and fearsome robbers. Gerda's power to face every obstacle in the quest to save her friend from his kidnapper, The Snow Queen, lies in her innocence and her abiding faith.Storyteller Hans Christian Andersen is famed for his heartwarming tales of enduring love and persistence in the face of adversity. Enchanting full-color images by Golden Age illustrator Edmund Dulac enhance Andersen's fairy tale of a girl's unshakable determination and stirring heroism, a classic that inspired the Disney animated film Frozen.

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This keepsake gift volume ranges from the twelfth century B.C. to modern times to present an international sampling of the world's best short poems. The works of ancient Greek, Latin, Hebrew, and Persian poets appear alongside those of Arabic, Chinese, German, Indian, Japanese, and Hungarian authors, in addition to classics by English, Irish, and American writers.Featured poems include those of Pushkin ("I Loved You"), Yeats ("Down by the Salley Gardens"), Jonson ("On My First Daughter"), Hughes ("The Negro Speaks of Rivers"), Basho ("The Quiet Pond"), Bhasa ("The Moon"), and Tsvetaeva ("I do not think, or argue, or complain"). Additional selections include verse by Li Po, Sappho, Paz, Shakespeare, Dickinson, Blake, Campion, H.D., Heine, Frost, Lermontov, Swift, Rilke, and many others.

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The Scientific Papers of James Clerk Maxwell, Vol. I

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One of the greatest theoretical physicists of the 19th century, James Clerk Maxwell is best known for his studies of the electromagnetic field. The 101 scientific papers of this two-volume set, arranged chronologically, testify to Maxwell's profound scientific legacy and include the preliminary explorations that culminated in his most famous work, A Treatise on Electricity and Magnetism.  One of the nineteenth century's most significant papers, "A Dynamical Theory of the Electromagnetic Field," appears here, along with similarly influential expositions of Maxwell's dynamical theory of gases. The author's extensive range of interests is well represented, from his discussions of color blindness and the composition of Saturn's rings to his essays on geometrical optics, ether, and protecting buildings from lightning. His less technical writings are featured as well, including items written for the Encyclopedia Britannica and Nature magazine, book reviews, and popular lectures. Striking in their originality, these papers offer a wealth of stimulating and inspiring reading to modern students of mathematics and physics.

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Rich in insights and inspiration, this anthology surveys the challenges and rewards of teaching. Contributions range from essays by renowned educators such as Pestalozzi, Froebel, Montessori, and Neill to the philosophical observations of Plato, Rousseau, Dewey, and Russell. Writings by Tolstoy, Emerson, and D. H. Lawrence appear alongside those of contemporary teachers, including Taylor Mali, Elizabeth Gold, and Philip Schultz, who reflect on their experiences with honesty, humor, and wonder.In addition to essays, this compilation draws upon letters, diaries, commencement addresses, memoirs, and poetry, all of which portray the dynamics of teaching. Editor Bob Blaisdell provides brief introductions to the contributors and their works and contributes an essay as well. Teachers, professors, and students will welcome this thought-provoking anthology, as will others interested in the history and philosophy of education.

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Don't know Socrates from Sartre? Can't handle Kant? This lively introduction traces the history of Western philosophy, from the works of Plato and Aristotle to those of Simone de Beauvoir and Michel Foucault. Easy-to-understand explanations cover all branches of philosophy, illustrating changing interpretations of the meaning of life and outlining key ideas of famous thinkers.Author Neil Turnbull offers memorable examples and analogies, injecting a playful modern tone into potentially obscure subjects. Loaded with sidebars, comic illustrations, and bulleted points, the book's reader-friendly format offers digestible portions from a banquet of philosophical traditions, including thought-provoking tastes of works by Aquinas, Descartes, Wittgenstein, Hume, Heidegger, Nietzsche, and many others.

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In 1943, while in charge of Columbia University's Statistical Research Group, Abraham Wald devised Sequential Design, an innovative statistical inference system. Because the decision to terminate an experiment is not predetermined, sequential analysis can arrive at a decision much sooner and with substantially fewer observations than equally reliable test procedures based on a predetermined number of observations. The system's immense value was immediately recognized, and its use was restricted to wartime research and procedures. In 1945, it was released to the public and has since revolutionized many aspects of statistical practice.This book is Professor Wald's own description of the system. Part I contains a discussion of the general theory of the sequential probability ratio test, with comparisons to traditional statistical inference systems. Part II discusses applications that illustrate the general theory and raise points of theoretical interest specific to these applications. Part III outlines a possible approach to the problem of sequential multi-valued decisions and estimation. All three sections can be understood by readers with only a background in college algebra and a first course in calculus. Mathematical derivations of somewhat intricate nature appear in the appendix.Sequential Analysis offers statistical researchers a time- and money-saving approach, introduces students to one of the major systems in contemporary use, and presents those already acquainted with the system with valuable background information.

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Leo Ornstein's Piano Sketch Books with Downloadable MP3s

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Progressive Pieces from Beginner to Intermediate

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Beginning pianists will rejoice in this collection of original, fun-to-play pieces by a noted American composer. First published between 1939 and 1945, the melodies provide an interesting and positive musical experience while building technical skills and sight reading. The songs start simply and incrementally, adding more complexity as students progress through the book.Virtuoso pianist Janice Weber provides additional guidance, and the collection comes with a separate MP3 download for each of the eighty-three pieces. Selections include "My Little Boat is Sailing," "Long Live the King," "Lets Go Skating," "The Lonely Cowboy," "The Viking Song," and other playful tunes. In addition to its value to beginning pianists of all ages, this collection is also helpful for those wishing to practice and refresh their skills.

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Leo Ornstein, Severo Ornstein, Janice Weber

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Expert toymaker Ted Menten shows how to make 14 cute little critters, each held together by snaps. The snappy approach allows mixing and matching of heads, arms, and legsand it assists with attaching a variety of charming accessories, including such seasonal items as valentines, Christmas stockings, and Easter eggs. Well-illustrated, simple instructions make assembling these lovable toys a snap!Beginners and veteran crafters alike will love creating these creatures, which include a puppy, lion, tiger, lamb, panda, squirrel, elephant, and other animals. Nothing expresses affection like a handcrafted present, and these adorable plush toys make wonderful, one-of-a-kind gifts.

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Few creatures of horror have seized readers' imaginations and held them for so long as the anguished monster of Mary Shelley's Frankenstein. The story of Victor Frankenstein's terrible creation and the havoc it caused has enthralled generations of readers and inspired countless writers of horror and suspense. Considering the novel's enduring success, it is remarkable that it began merely as a whim of Lord Byron's."We will each write a story," Byron announced to his next-door neighbors, Mary Wollstonecraft Godwin and her lover Percy Bysshe Shelley. The friends were summering on the shores of Lake Geneva in Switzerland in 1816, Shelley still unknown as a poet and Byron writing the third canto of Childe Harold. When continued rains kept them confined indoors, all agreed to Byron's proposal.The illustrious poets failed to complete their ghost stories, but Mary Shelley rose supremely to the challenge. With Frankenstein, she succeeded admirably in the task she set for herself: to create a story that, in her own words, "would speak to the mysterious fears of our nature and awaken thrilling horror  one to make the reader dread to look round, to curdle the blood, and quicken the beatings of the heart."

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Solid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. Author David J. Winter, a Professor of Mathematics at the University of Michigan, also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields.Preliminary material covers modules and nonassociate algebras, followed by a compact, self-contained development of the theory of Lie algebras of characteristic 0. Topics include solvable and nilpotent Lie algebras, Cartan subalgebras, and Levi's radical splitting theorem and the complete reducibility of representations of semisimple Lie algebras. Additional subjects include the isomorphism theorem for semisimple Lie algebras and their irreducible modules, automorphism of Lie algebras, and the conjugacy of Cartan subalgebras and Borel subalgebras. An extensive theory of Cartan and related subalgebras of Lie algebras over arbitrary fields is developed in the final chapter, and an appendix offers background on the Zariski topology.

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This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras.A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract definition of shape theory. Upon returning to the geometric base, the text considers simplical complexes and numerable covers, in addition to Morita's form of shape theory. Subsequent chapters explore Benabou's theory of distributors, the theory of exact squares, Kan extensions, the notion of a stable object, and stability in an Abelian context. The text concludes with a brief description of derived functors of the limit functor theorythe concept that leads to movability and strong movability of systemsand illustrations of the equivalence of strong movability and stability in many contexts.

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One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The texts first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimensions. Additional topics include least squares and other Galerkin methods. Many helpful definitions, examples, and exercises appear throughout the book. A classic reference in spline theory, this volume will benefit experts as well as students of engineering and mathematics.

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Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. Only a slight acquaintance with mathematics beyond the high-school level is necessary, including some familiarity with calculus and linear algebra. This text's introductions to several branches of geometry feature topics and treatments based on memorability and relevance. The author emphasizes connections with calculus and simple mechanics, focusing on developing students' grasp of spatial relationships. Subjects include classical Euclidean material, polygonal and circle isoperimetry, conics and Pascal's theorem, geometrical optimization, geometry and trigonometry on a sphere, graphs, convexity, and elements of differential geometry of curves. Additional material may be conveniently introduced in several places, and each chapter concludes with exercises of varying degrees of difficulty.