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The lecture series on the Theory of the Top was originally given as a dedication to Göttingen University by Felix Klein in 1895, but has since found broader appeal. The Theory of the Top: Volume I. Introduction to the Kinematics and Kinetics of the Top is the first of a series of four self-contained English translations that provide insights into kinetic theory and kinematics.
This book is a comprehensive treatment of engineering undergraduate differential equations as well as linear vibrations and feedback control. While this material has traditionally been separated into different courses in undergraduate engineering curricula. This text provides a streamlined and efficient treatment of material normally covered in three courses. Ultimately, engineering students study mathematics in order to be able to solve problems within the engineering realm. Engineering Differential Equations: Theory and Applications guides students to approach the mathematical theory with much greater interest and enthusiasm by teaching the theory together with applications. Additionally, it includes an abundance of detailed examples. Appendices include numerous C and FORTRAN example programs. This book is intended for engineering undergraduate students, particularly aerospace and mechanical engineers and students in other disciplines concerned with mechanical systems analysis and control. Prerequisites include basic and advanced calculus with an introduction to linear algebra.
Activity theory holds that the human mind is the product of our interaction with people & artifacts in everyday activity. This book makes the case for activity theory as a basis for understanding our relationship with technology. It describes activity theory's principles, history, & relationship to other theoretical approaches.
The breadth of matrix theory's applications is reflected by this volume, which features material of interest to applied mathematicians as well as to control engineers studying stability of a servo-mechanism and numerical analysts evaluating the roots of a polynomial. Starting with a survey of complex symmetric, antisymmetric, and orthogonal matrices, the text advances to explorations of singular bundles of matrices and matrices with nonnegative elements. Applied mathematicians will take particular note of the full and readable chapter on applications of matrix theory to the study of systems of linear differential equations, and the text concludes with an exposition on the Routh-Hurwitz problem plus several helpful appendixes. 1959 edition.
​​​The importance of benchmarking in the service sector is well recognized as it helps in continuous improvement in products and work processes. Through benchmarking, companies have strived to implement best practices in order to remain competitive in the product- market in which they operate. However studies on benchmarking, particularly in the software development sector, have neglected using multiple variables and therefore have not been as comprehensive. Information Theory and Best Practices in the IT Industry fills this void by examining benchmarking in the business of software development and studying how it is affected by development process, application type, hardware platforms used, and many other variables. Information Theory and Best Practices in the IT Industry begins by examining practices of benchmarking productivity and critically appraises them. Next the book identifies different variables which affect productivity and variables that affect quality, developing useful equations that explaining their relationships. Finally these equations and findings are applied to case studies. Utilizing this book, practitioners can decide about what emphasis they should attach to different variables in their own companies, while seeking to optimize productivity and defect density.
This book presents a comprehensive and unifying theory to promote the under standing of technical systems. Such a theory is useful as a foundation for a ratio nal approach to the engineering design process, as a background to engineering education, and other applications. The term "technical system" is used to represent all types of man-made artifacts, including technical products and processes. The technical system is therefore the subject (in the grammatical sense of the word) of the collection of activities which are performed by engineers within the processes of engineering design, including generating, retrieving, processing and transmitting of information about products. It is also the subject of various tasks in the production process, including work preparation and production planning, and in many economic considerations, company-internal and societal. In this way, the Theory of Technical Systems is a contribution to science, as in terpreted in the wider, Germanic sense of a "co-ordinated and codified body of knowledge". It brings together the various viewpoints of engineers, scientists, economists, ergonomists, managers, users, sociologists, etc., and shows where and how they influence the forms of engineering products. It also explains the influ ences that a product exerts on its environment. This Theory of Technical Systems should thus interest design engineers, and en gineers involved in production, management, sales, etc. In an interdisciplinary ap plication of value analysis, the Theory of Technical Systems should provide answers to many questions raised in this field.
About Felix Klein, the famous Greek mathematician Constantin Carathéodory once said: “It is only by illuminating him from all angles that one can come to understand his significance.” The author of this biography has done just this. A detailed study of original sources has made it possible to uncover new connections; to create a more precise representation of this important mathematician, scientific organizer, and educational reformer; and to identify misconceptions. Because of his edition of Julius Plücker’s work on line geometry and due to his own contributions to non-Euclidean geometry, Klein was already well known abroad before he received his first full professorship at the age of 23. By exchanging ideas with his most important cooperation partner, the Norwegian Sophus Lie, Klein formulated his Erlangen Program. Various other visionary programs followed, in which Klein involved mathematicians from Germany and abroad. Klein was the most active promoter of Riemann’s geometric-physical approach to function theory, but he also integrated the analytical approaches of the Weierstrass school into his arsenal of methods. Klein was a citizen of the world who repeatedly travelled to France, Great Britain, Italy, the United States, and elsewhere. Despite what has often been claimed, it must be emphasized that Klein expressly opposed national chauvinism. He promoted mathematically gifted individuals regardless of their nationality, religion, or gender. Many of his works have been translated into English, French, Italian, Russian, and other languages; more than 300 supporters from around the world made it possible for his portrait to be painted by the prominent impressionist Max Liebermann. Inspired by international developments, Klein paved the way for women to work in the field of mathematics. He was instrumental in reforming mathematical education, and he endorsed an understanding of mathematics that affirmed its cultural importance as well as its fundamental significance to scientific and technological progress.
Suh (mechanical engineering, Massachusetts, Institute of Technology) offers a general theoretical framework that may be used to solve complexity problems in engineering, science, and even in certain nontechnical areas.
An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs—categories in disguise. After explaining the “big three” concepts of category theory—categories, functors, and natural transformations—the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.