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Self-contained and suitable for undergraduate students, this text offers a working knowledge of calculus and statistics. It assumes only a familiarity with basic analytic geometry, presenting a coordinated study that develops the interrelationships between calculus, probability, and statistics.Starting with the basic concepts of function and probability, the text addresses some specific probabilities and proceeds to surveys of random variables and graphs, the derivative, applications of the derivative, sequences and series, and integration. Additional topics include the integral and continuous variates, some basic discrete distributions, as well as other important distributions, hypothesis testing, functions of several variables, and regression and correlation. The text concludes with an appendix, answers to selected exercises, a general index, and an index of symbols.
"His lively pen, his direct and simple style, his expressive vocabulary, his avoidance of pedantry, his conciseness in the exposition of his thoughts make his book a pleasure to read." -- Henri Michel, International Academy of the History of ScienceThe story of man's efforts to measure time is a long one -- reaching back thousands of years to the dawn of civilization. Among the earliest instruments developed for telling time was the sundial. In this expert study, a noted sundial expert offers a fascinating and informative account of these ancient devices, presented in simple, lively language.Over the centuries, many different varieties of sundials have been constructed, and Mr. Rohr provides detailed, accurate descriptions of them all: classical sundials, inclined dials, solar calendars, analemmatic dials, moon dials, and many more. There is even a chapter devoted to especially remarkable dials past and present, and a listing of the most popular sundial mottoes. In this profusely illustrated volume, you will not only learn about the long and colorful history of the sundial, you will learn a practical method of building one yourself. No special knowledge is required, other than an understanding of the basic principles of cosmography and of the relative movements of the sun and the planets. (These are recalled in an elementary way in a special chapter.) For mathematically inclined readers, more complex formulae and calculations have been included, some of which have never been printed in a book of gnomonics.
From his unusual beginning in "Defining a vector" to his final comments on "What then is a vector?" author Banesh Hoffmann has written a book that is provocative and unconventional. In his emphasis on the unresolved issue of defining a vector, Hoffmann mixes pure and applied mathematics without using calculus. The result is a treatment that can serve as a supplement and corrective to textbooks, as well as collateral reading in all courses that deal with vectors. Major topics include vectors and the parallelogram law; algebraic notation and basic ideas; vector algebra; scalars and scalar products; vector products and quotients of vectors; and tensors. The author writes with a fresh, challenging style, making all complex concepts readily understandable. Nearly 400 exercises appear throughout the text. Professor of Mathematics at Queens College at the City University of New York, Banesh Hoffmann is also the author of The Strange Story of the Quantum and other important books. This volume provides much that is new for both students and their instructors, and it will certainly generate debate and discussion in the classroom.
Students learn how to read and write proofs by actually reading and writing them, asserts author Joseph J. Rotman, adding that merely reading about mathematics is no substitute for doing mathematics. In addition to teaching how to interpret and construct proofs, Professor Rotman's introductory text imparts other valuable mathematical tools and illustrates the intrinsic beauty and interest of mathematics.Journey into Mathematics offers a coherent story, with intriguing historical and etymological asides. The three-part treatment begins with the mechanics of writing proofs, including some very elementary mathematics--induction, binomial coefficients, and polygonal areas--that allow students to focus on the proofs without the distraction of absorbing unfamiliar ideas at the same time. Once they have acquired some geometric experience with the simpler classical notion of limit, they proceed to considerations of the area and circumference of circles. The text concludes with examinations of complex numbers and their application, via De Moivre's theorem, to real numbers.
Comprehensive and complete, this overview provides a single-volume treatment of key algorithms and theories. The author provides clear explanations of all theoretical aspects, with rigorous proof of most results. The two-part treatment begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs. The second part concerns techniques for numerical solutions and unconstrained optimization methods, and it presents commonly used algorithms for constrained nonlinear optimization problems. This graduate-level text requires no advanced mathematical background beyond elementary calculus, linear algebra, and real analysis. 1976 edition. 58 figures. 7 tables.
More than a graduate text and advanced research guide on condensed matter physics, this volume is useful to plasma physicists and polymer chemists, and their students. It emphasizes applications of statistical mechanics to a variety of systems in condensed matter physics rather than theoretical derivations of the principles of statistical mechanics and techniques. Isihara addresses a dozen different subjects in separate chapters, each designed to be directly accessible and used independently of previous chapters. Topics include simple liquids, electron systems and correlations, two-dimensional electron systems, quasi one-dimensional systems, hopping and localization, magnetism, superconductivity, liquid helium, liquid crystals, and polymers. Extensive appendixes offer background on molecular distribution functions, which play important roles in the theoretical derivations.
Combining fractal theory with computer art, this book introduces a creative use of computers. It describes graphic methods for detecting patterns in complicated data and illustrates simple techniques for visualizing chaotic behavior. "Beautiful." -- Martin Gardner, Scientific American. Over 275 illustrations, 29 in color.
One of the twentieth century's most original mathematicians and thinkers, Karl Menger taught students of many backgrounds. In this, his radical revision of the traditional calculus text, he presents pure and applied calculus in a unified conceptual frame, offering a thorough understanding of theory as well as of the methodology underlying the use of calculus as a tool.The most outstanding feature of this text is the care with which it explains basic ideas, a feature that makes it equally suitable for beginners and experienced readers. The text begins with a "mini-calculus" which brings out the fundamental results without recourse to the notions of limit and continuity. The standard subject matter is then presented as a pure and unambiguous calculus of functions. The issues surrounding the applications of pure calculus to problems in the sciences are faced in a forthright manner by carefully analyzing the meaning of "variable quantity" and clarified by resuscitating Newton's concept of fluents. The accompanying exercises are original, insightful and an integral part of the text. This Dover edition features a new Preface and Guide to Further Reading by Bert Schweizer and Abe Sklar.
This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of weak derivatives, proves various inequalities and imbedding problems, and derives smoothness theorems. Part Two concerns evolution equations in Banach space and develops the theory of semigroups. It solves the initial-boundary value problem for parabolic equations and covers backward uniqueness, asymptotic behavior, and lower bounds at infinity. The final section includes independent topics directly related to the methods and results of the previous material, including the analyticity of solutions of elliptic and parabolic equations, asymptotic behavior of solutions of elliptic equations near infinity, and problems in the theory of control in Banach space.
This classic graduate-level volume was the first general but simple introduction to the fields of plasma and fusion research. Since its original publication in 1956, it has served as a valuable reference. Designed for those who have had an introductory course in theoretical physics but are otherwise unacquainted with the detailed kinetic theory of gases, it chiefly emphasizes macroscopic equations and their consequences.The contents are restricted to topics offering a theoretical understanding of plasma and fusion research. Subjects include the motion of a particle, macroscopic behavior of a plasma, waves in a plasma, equilibria and their stability, and encounters between changed particles. A helpful appendix offers background on the Boltzmann equation.Author Lyman Spitzer, Jr., was the first to propose the idea of placing a large telescope in space, and he was the driving force behind the development of the Hubble Space Telescope. Founder and director of Princeton's Plasma Physics Laboratory, a pioneering program in controlled thermonuclear research, Spitzer taught and inspired a generation of plasma physicists.
"Highly recommended. . . . This is an important book in putting the burgeoning field of sociodynamics on a solid footing."--Journal of Artificial Societies and Social SimulationThis text deals with general modelling concepts in the social sciences, their applications, and their mathematical methods. The author's well-organized approach offers a clear, coherent introduction to terminology, approaches, and goals in modelling. Appropriate for advanced undergraduates and graduate students, it requires a solid background in algebra and calculus.The three-part treatment begins by addressing general modelling concepts, the second part provides applications, and the third discusses mathematical method. Topics include population dynamics, group interaction, political transitions, evolutionary economics, and urbanization. Guiding students through a series of practical applications that illustrate the methods' potential scope, the text concludes with a detailed look at mathematical methods.
280 problems, with detailed solutions, plus 139 exercises, all covering quantum mechanics, wave mechanics, angular momentum, molecular spectroscopy, scattering theory, and related subjects. "An excellent problem book . . . I would highly recommend it as a required supplement to students taking their first quantum chemistry course." -- Journal of the American Chemical Society.
Although mathematical logic can be a formidably abstruse topic, even for mathematicians, this concise book presents the subject in a lively and approachable fashion. It deals with the very important ideas in modern mathematical logic without the detailed mathematical work required of those with a professional interest in logic.The book begins with a historical survey of the development of mathematical logic from two parallel streams: formal deduction, which originated with Aristotle, Euclid, and others; and mathematical analysis, which dates back to Archimedes in the same era. The streams began to converge in the seventeenth century with the invention of the calculus, which ultimately brought mathematics and logic together. The authors then briefly indicate how such relatively modern concepts as set theory, Gödel's incompleteness theorems, the continuum hypothesis, the Löwenheim-Skolem theorem, and other ideas influenced mathematical logic. The ideas are set forth simply and clearly in a pleasant style, and despite the book's relative brevity, there is much covered on these pages. Nonmathematicians can read the book as a general survey; students of the subject will find it a stimulating introduction. Readers will also find suggestions for further reading in this lively and exciting area of modern mathematics.
"This is a very good book ... with many well-chosen examples and illustrations." -- American Mathematical MonthlyThis highly regarded text presents a self-contained introduction to some important aspects of modern qualitative theory for ordinary differential equations. It is accessible to any student of physical sciences, mathematics or engineering who has a good knowledge of calculus and of the elements of linear algebra. In addition, algebraic results are stated as needed; the less familiar ones are proved either in the text or in appendixes.The topics covered in the first three chapters are the standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. The next three chapters, the heart of the book, deal with stability theory and some applications, such as oscillation phenomena, self-excited oscillations and the regulator problem of Lurie.One of the special features of this work is its abundance of exercises-routine computations, completions of mathematical arguments, extensions of theorems and applications to physical problems. Moreover, they are found in the body of the text where they naturally occur, offering students substantial aid in understanding the ideas and concepts discussed. The level is intended for students ranging from juniors to first-year graduate students in mathematics, physics or engineering; however, the book is also ideal for a one-semester undergraduate course in ordinary differential equations, or for engineers in need of a course in state space methods.
This introduction to combinatorics, the foundation of the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics.The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises.
This concise volume offers undergraduates an introduction to mathematical formalism in problems of molecular structure and motion. The main topics cover the calculus of orthogonal functions, algebra of vector spaces, and Lagrangian and Hamiltonian formulation of classical mechanics and applications to molecular motion. Answers to problems. 1966 edition.
Beginning text presents complete theoretical treatment of mechanical model systems and deals with technological applications. Topics include introduction to calculus of vectors, particle motion, dynamics of particle systems and plane rigid bodies, technical applications in plane motions, theory of mechanical vibrations, and more. Exercises and answers appear in each chapter.
Since the discovery that each particular antibody in the blood tends to react primarily with one specific antigen among the hundreds that can be introduced into the system, great strides have been made toward the elimination of disease through immunization. The late Dr. Karl Landsteiner, winner of the Nobel Price in 1930 for the discovery of human blood groups, devoted his life to fundamental research and played a guiding role in the development of several important branches of immunology. This authoritative study is an account of the experiments he and his colleagues carried out on antigens and serological reactions with simple compounds. Beginning with a general discussion of the phenomena of serological specificity, with the emphasis chiefly on the chemical aspects of those reactions that involve immunization, Dr. Landsteiner goes on to cover the topics of natural antigens and antibodies, artificial conjugated antigens, and the reactivity of simple chemical compounds, the chemistry of specific non-protein cell substances, and the developments in our knowledge of serological reactions from a physico-chemical approach. Included in the discussion are his original and fundamental studies in hypersensitivity to chemical allergens and his work with "haptens," on which modern immunochemistry has leaned very heavily. The final chapter, written by Dr. Linus Pauling, carefully presents the principles of molecular structure and intermolecular forces. An extremely valuable feature of this book is the massive bibliography compiled by the author -- over 2,100 items are listed at the chapter ends. A further aid to study and research is the definitive bibliography of Dr. Landsteiner's own writings, new to this edition, and reprinted through the courtesy of the Journal of Immunology. The beginner and advanced student alike will find nowhere else the breadth of coverage given here to basic concepts of immunology. Comprehensive enough for the use of the worker in the field, the book also provides, primarily in an introductory section, explanations and definitions of elementary terminology, concepts, and phenomena of serology for those unacquainted with the subject.
Rates and Equilibria of Organic Reactions: As Treated by Statistical, Thermodynamic and Extrathermodynamic Methodsby Ernest Grunwald John E. Leffler
Graduate-level text stresses extrathermodynamic approach to quantitative prediction and constructs a logical framework that encompasses and classifies all known extrathermodynamic relationships. Numerous figures and tables. Author and Subject Indexes.
This guide is guaranteed to prove of keen interest to the broad spectrum of experimental chemists who use electronic structure theory to assist in the interpretation of their laboratory findings. A list of 150 landmark papers in ab initio molecular electronic structure methods, it features the first page of each paper (which usually encompasses the abstract and introduction). Its primary focus is methodology, rather than the examination of particular chemical problems, and the selected papers either present new and important methods or illustrate the effectiveness of existing methods in predicting a variety of chemical phenomena.
Fluid dynamics, the behavior of liquids and gases, is a field of broad impact that encompasses aspects of physics, engineering, oceanography, and meteorology. Full understanding demands fluency in higher mathematics, the only language of fluid dynamics. This introductory text is geared toward advanced undergraduate and graduate students in applied mathematics, engineering, and the physical sciences. It assumes a knowledge of calculus and vector analysis.Author Richard E. Meyer notes, "This core of knowledge concerns the relation between inviscid and viscous fluids, and the bulk of this book is devoted to a discussion of that relation." Dr. Meyer develops basic concepts from a semi-axiomatic foundation, observing that such treatment helps dispel the common impression that the entire subject is built on a quicksand of assorted intuitions. His topics include kinematics, momentum principle and ideal fluid, Newtonian fluid, fluids of small viscosity, some aspects of rotating fluids, and some effects of compressibility. Each chapter concludes with a set of problems.
Students of mathematical biology discover modern methods of taxonomy with this text, which introduces taxonomic characters, the measurement of similarity, and the analysis of principal components. Other topics include multidimensional scaling, cluster analysis, identification and assignment techniques, more. A familiarity with matrix algebra and elementary statistics are the sole prerequisites.
"My heart always sinks within me when I hear the good housewife, of every class, say, 'I assure you the bed has been well slept in: and I can only hope it is not true. What? Is the bed already saturated with somebody else's damp before my patient comes to exhale in it his own damp? Has it not had a single chance to be aired? No, not one. It has been slept in every night."From the best known work of Florence Nightingale (1820-1910), the originator and founder of modern nursing, comes a collection of notes that played an important part in the much needed revolution in the field of nursing. For the first time it was brought to the attention of those caring for the sick that their responsibilities covered not only the administration of medicines and the application of poultices, but the proper use of fresh air, light, warmth, cleanliness, quiet, and the proper selection and administration of diet. Miss Nightingale is outspoken on these subjects as well as on other factors that she considers essential to good nursing. But, whatever her topic, her main concern and attention is always on the patient and his needs.One is impressed with the fact that the fundamental needs of the sick as observed by Miss Nightingale are amazingly similar today (even though they are generally taken for granted now) to what they were over 100 years ago when this book was written. For this reason, this little volume is as practical as it is interesting and entertaining. It will be an inspiration to the student nurse, refreshing and stimulating to the experienced nurse, and immensely helpful to anyone caring for the sick.
With some 70 percent of its surface covered by water, the Earth presents a picture of a gemlike blue planet when viewed from outer space. This sapphire jewel -- the only planet in our solar system to sustain intelligent life -- is the subject of this remarkably engaging and concise book by biologist, teacher, and popular science writer Url Lanham. Focusing on the Earth and the life forms that have evolved on it, Mr. Lanham's captivating study covers a wide range of subjects -- from the work of Galileo, Copernicus, Herschel, and other scientists who contributed to our knowledge of Earth's position in the universe, to the Earth's internal physiology, intricacies of the biosphere, creation of continents, origins of plant and animal life, the diversity of physical habitats in which these life forms thrive, and much more. Well written and highly readable, this absorbing and optimistic natural history of the planet will take readers on a fantastic journey through time, offering up a host of facts and provocative insights. Easily accessible to advanced high school science students and college undergraduates, Earth, the Sapphire Planet will be warmly received as well by teachers and ecologically aware general readers.
This inspiring and enriching book, a collection of essays that evokes the beauty and wonder of the night sky, explains to beginning skywatchers how to find and where to look for specific celestial objects. Author Fred Schaaf, once described as a naturalist in the tradition of Henry David Thoreau and John Burroughs, reveals an intense love of his subject and a keen knowledge of the optimum ways of viewing astronomical phenomena with the naked eye. Schaaf not only describes such special sights as an eyelash-thin moon, a shooting star, streaking comets, and a lunar eclipse, but he also explains when and where to look for constellations and planetary conjunctions, meteor showers, rainbows, halos, and other celestial occurrences. Most of these observations require no telescopes or other equipment, not even perfect sky conditions or long periods of special training. Technical expressions are explained as they appear in the text, and a glossary at the end defines terms and concepts.Astronomy magazine advises anyone interested in stargazing to "find a place for [this book] on your library shelf"; and Chet Raymo, author of 365 Starry Nights, says "this is a book that will help define amateur astronomy."
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