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Clear, lively style covers all basics of theory and application, including mathematical models, elementary concepts of graph theory, transportation problems, connection problems, party problems, diagraphs and mathematical models, games and puzzles, graphs and social psychology, planar graphs and coloring problems, and graphs and other mathematics.
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Julian Havil is a former Master at Winchester College, England, where he taught mathematics for more than thirty years. He is the author of Gamma: Exploring Euler's Constant and Impossible?: Surprising Solutions to Counterintuitive Conundrums (both Princeton).
Math-the application of reasonable logic to reasonable assumptions-usually produces reasonable results. But sometimes math generates astonishing paradoxes-conclusions that seem completely...
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Brief but intriguing, this monograph on the theory of elliptic functions was written by one of America's most prominent and widely read mathematicians. Richard Bellman encompasses a wealth of material in a succession of short chapters, spotlighting high points of the fundamental regions of elliptic functions and illustrating powerful and versatile analytic methods. Suitable for advanced undergraduates and graduate students in mathematics, this introductory...
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This excellent text introduces the use of exterior differential forms as a powerful tool in the analysis of a variety of mathematical problems in the physical and engineering sciences. Requiring familiarity with several variable calculus and some knowledge of linear algebra and set theory, it is directed primarily to engineers and physical scientists, but it has also been used successfully to introduce modern differential geometry to students in mathematics....
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"One of Choice's Outstanding Academic Titles for 1997" Florin Diacu is Associate Professor of Mathematics at the University of Victoria in Canada. Philip Holmes, a Fellow of the American Academy of Arts and Sciences, is Professor of Mechanics and Applied Mathematics at Princeton University, where he directs the Program in Applied and Computational Mathematics.
Celestial Encounters is for anyone who has ever wondered about the foundations of chaos....
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An early but still useful and frequently cited contribution to the science of mathematical economics, this volume is geared toward graduate students in the field. Prerequisites include familiarity with the basic theory of matrices and linear transformations and with elementary calculus. Author Jacob T. Schwartz begins his treatment with an exploration of the Leontief input-output model, which forms a general framework for subsequent material. An introductory...
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This book can be used as either a primary text or a supplemental reference for courses in applied mathematics. Its core chapters are devoted to linear algebra, calculus, and ordinary differential equations. Additional topics include partial differential equations and approximation methods. Each chapter features an ample selection of solved problems. These problems were chosen to illustrate not only how to solve various algebraic and differential equations...
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This graduate-level text's primary objective is to demonstrate the expression of the equations of the various branches of mathematical physics in the succinct and elegant form of variational principles (and thereby illuminate their interrelationship). Its related intentions are to show how variational principles may be employed to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities...
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Assuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. Topics include the representation theorem and distribution...
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This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject,...
11) Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management
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An excellent financial research tool, this classic focuses on the methods of solving continuous time problems. The two-part treatment covers closely related approaches to the calculus of variations and optimal control. In the two decades since its initial publication, the text has defined dynamic optimization for courses in economics and management science. Simply, clearly, and succinctly written chapters introduce new developments, expound upon underlying...
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This book offers advanced undergraduates and graduate students in physics, engineering, and other natural sciences a solid foundation in several fields of mathematics. Clear and well-written, it assumes a previous knowledge of the theory of functions of real and complex variables, and is ideal for classroom use, self-study, or as a supplementary text. Starting with vector spaces and matrices, the text proceeds to orthogonal functions; the roots of...
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Los mayores desafíos de la humanidad actual se arraigan en las múltiples e intrincadas relaciones entre nuestra sociedad y el mundo natural. Y a esta complejidad inherente —que emerge de las intersecciones de la física con la biología, la psicología, la sociología y la economía, entre otras disciplinas—, se suma el ser esquiva al razonamiento intuitivo. De ahí la importancia de contar con herramientas teóricas y técnicas que permitan...
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Written by a pioneer in the development of reliability methods, this text applies statistical mathematics to the analysis of electrical, mechanical, and other systems employed in airborne, missile, and ground equipment. Geared toward upper-level undergraduate and graduate students, it is also a valuable reference for professionals. 1961 edition.
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Suitable for advanced undergraduate and graduate students, this text offers detailed considerations of general theorems, conservation equations, waves, shocks, and nonisentropic flows, with emphasis on the basics, both conceptual and mathematical. The general theory of characteristics receives a remarkably complete and simple treatment, with detailed applications. 175 figures. 1958 edition.
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Based on the author's lectures at the University of Bonn in 1983–84, this book introduces classical scattering theory and the time-dependent theory of linear equations in mathematical physics. Topics include proof of the existence of wave operators, some special equations of mathematical physics, exterior boundary value problems, radiation conditions, and limiting absorption principles.
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This distinctly nonclassical treatment focuses on developing aspects that differ from the theory of ordinary metric spaces, working directly with probability distribution functions rather than random variables. The two-part treatment begins with an overview that discusses the theory's historical evolution, followed by a development of related mathematical machinery. The presentation defines all needed concepts, states all necessary results, and provides...
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This introductory text is geared toward engineers, physicists, and applied mathematicians at the advanced undergraduate and graduate levels. It applies the mathematics of Cartesian and general tensors to physical field theories and demonstrates them chiefly in terms of the theory of fluid mechanics. Numerous exercises appear throughout the text. 1962 edition.
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This advanced text explores a category of mathematical problems that occur frequently in physics and other sciences. Five preliminary chapters make the book accessible to students without extensive background in this area. Topics include Hamiltonian systems, symplecticness, numerical methods, order conditions, and implementation. The heart of the book, chapters 6 through 10, explores simplistic integration, simplistic order conditions, available simplistic...
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