Dimensional Analysis
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| Author | : Juan G. Santiago |
| Publisher | : MIT Press |
| Total Pages | : 179 |
| Release | : 2019-10-22 |
| Genre | : Technology & Engineering |
| ISBN | : 0262355108 |
An introduction to dimensional analysis, a method of scientific analysis used to investigate and simplify complex physical phenomena, demonstrated through a series of engaging examples. This book offers an introduction to dimensional analysis, a powerful method of scientific analysis used to investigate and simplify complex physical phenomena. The method enables bold approximations and the generation of testable hypotheses. The book explains these analyses through a series of entertaining applications; students will learn to analyze, for example, the limits of world-record weight lifters, the distance an electric submarine can travel, how an upside-down pendulum is similar to a running velociraptor, and the number of Olympic rowers required to double boat speed. The book introduces the approach through easy-to-follow, step-by-step methods that show how to identify the essential variables describing a complex problem; explore the dimensions of the problem and recast it to reduce complexity; leverage physical insights and experimental observations to further reduce complexity; form testable scientific hypotheses; combine experiments and analysis to solve a problem; and collapse and present experimental measurements in a compact form. Each chapter ends with a summary and problems for students to solve. Taken together, the analyses and examples demonstrate the value of dimensional analysis and provide guidance on how to combine and enhance dimensional analysis with physical insights. The book can be used by undergraduate students in physics, engineering, chemistry, biology, sports science, and astronomy.
| Author | : Don S. Lemons |
| Publisher | : Cambridge University Press |
| Total Pages | : 115 |
| Release | : 2017-03-16 |
| Genre | : Mathematics |
| ISBN | : 1107161150 |
This introduction to dimensional analysis covers the methods, history and formalisation of the field. Utilising topics including mechanics, hydro- and electrodynamics, and thermal and quantum physics, it illustrates the possibilities and limitations of dimensional analysis, making it perfect for students on introductory courses in physics, engineering and mathematics.
| Author | : J.C. Gibbings |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 302 |
| Release | : 2011-02-11 |
| Genre | : Mathematics |
| ISBN | : 1849963177 |
For experiments, dimensional analysis enables the design, checks the validity, orders the procedure and synthesises the data. Additionally it can provide relationships between variables where standard analysis is not available. This widely valuable analysis for engineers and scientists is here presented to the student, the teacher and the researcher. It is the first complete modern text that covers developments over the last three decades while closing all outstanding logical gaps. Dimensional Analysis also lists the logical stages of the analysis, so showing clearly the care to be taken in its use while revealing the very few limitations of application. As the conclusion of that logic, it gives the author's original proof of the fundamental and only theorem. Unlike past texts, Dimensional Analysis includes examples for which the answer does not already exist from standard analysis. It also corrects the many errors present in the existing literature by including accurate solutions. Dimensional Analysis is written for all branches of engineering and science as a teaching book covering both undergraduate and postgraduate courses, as a guide for the lecturer and as a reference volume for the researcher.
| Author | : Hans G. Hornung |
| Publisher | : Courier Corporation |
| Total Pages | : 80 |
| Release | : 2013-01-18 |
| Genre | : Science |
| ISBN | : 048615047X |
Derived from a course in fluid mechanics, this text for advanced undergraduates and graduate students employs symmetry arguments to illustrate the principles of dimensional analysis. 2006 edition.
| Author | : Thomas Szirtes |
| Publisher | : Butterworth-Heinemann |
| Total Pages | : 853 |
| Release | : 2007-04-27 |
| Genre | : Technology & Engineering |
| ISBN | : 0080555454 |
Applied Dimensional Analysis and Modeling provides the full mathematical background and step-by-step procedures for employing dimensional analyses, along with a wide range of applications to problems in engineering and applied science, such as fluid dynamics, heat flow, electromagnetics, astronomy and economics. This new edition offers additional worked-out examples in mechanics, physics, geometry, hydrodynamics, and biometry. Covers 4 essential aspects and applications: principal characteristics of dimensional systems, applications of dimensional techniques in engineering, mathematics and geometry, applications in biosciences, biometry and economics, applications in astronomy and physics Offers more than 250 worked-out examples and problems with solutions Provides detailed descriptions of techniques of both dimensional analysis and dimensional modeling
| Author | : William G. Jacoby |
| Publisher | : SAGE |
| Total Pages | : 100 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : 9780803941786 |
For many readers, data theory is probably unfamiliar. Data isn't usually the subject matter of theory in and of itself. However, in this volume, William Jacoby introduces a theory of data idea. It examines how real world observations are transformed into something to be analyzed that is, data. Jacoby explores some of the basic ideas of data theory, and considers their implications for research strategies in the social sciences. "Like others in the series, it is reassuringly slim. It is intended for a general social science readership and is a worthwhile read even for experienced data analysts. since it draws attention not only to often overlooked assumptions, but also to often ignored analysis possibilities." --Telephone Surveys "On the whole, this book contains a lot of useful information." --Journal of Classification
| Author | : Giuseppe Da Prato |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 217 |
| Release | : 2006-08-25 |
| Genre | : Mathematics |
| ISBN | : 3540290214 |
Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.
| Author | : Volker Simon |
| Publisher | : Springer |
| Total Pages | : 144 |
| Release | : 2017-02-09 |
| Genre | : Technology & Engineering |
| ISBN | : 3319520288 |
This monograph provides the fundamentals of dimensional analysis and illustrates the method by numerous examples for a wide spectrum of applications in engineering. The book covers thoroughly the fundamental definitions and the Buckingham theorem, as well as the choice of the system of basic units. The authors also include a presentation of model theory and similarity solutions. The target audience primarily comprises researchers and practitioners but the book may also be suitable as a textbook at university level.
| Author | : John Wright |
| Publisher | : Cambridge University Press |
| Total Pages | : 718 |
| Release | : 2022-01-13 |
| Genre | : Computers |
| ISBN | : 1108805558 |
Connecting theory with practice, this systematic and rigorous introduction covers the fundamental principles, algorithms and applications of key mathematical models for high-dimensional data analysis. Comprehensive in its approach, it provides unified coverage of many different low-dimensional models and analytical techniques, including sparse and low-rank models, and both convex and non-convex formulations. Readers will learn how to develop efficient and scalable algorithms for solving real-world problems, supported by numerous examples and exercises throughout, and how to use the computational tools learnt in several application contexts. Applications presented include scientific imaging, communication, face recognition, 3D vision, and deep networks for classification. With code available online, this is an ideal textbook for senior and graduate students in computer science, data science, and electrical engineering, as well as for those taking courses on sparsity, low-dimensional structures, and high-dimensional data. Foreword by Emmanuel Candès.
| Author | : Charalambos D. Aliprantis |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 623 |
| Release | : 2013-11-11 |
| Genre | : Business & Economics |
| ISBN | : 3662030047 |
This text was born out of an advanced mathematical economics seminar at Caltech in 1989-90. We realized that the typical graduate student in mathematical economics has to be familiar with a vast amount of material that spans several traditional fields in mathematics. Much of the mate rial appears only in esoteric research monographs that are designed for specialists, not for the sort of generalist that our students need be. We hope that in a small way this text will make the material here accessible to a much broader audience. While our motivation is to present and orga nize the analytical foundations underlying modern economics and finance, this is a book of mathematics, not of economics. We mention applications to economics but present very few of them. They are there to convince economists that the material has so me relevance and to let mathematicians know that there are areas of application for these results. We feel that this text could be used for a course in analysis that would benefit math ematicians, engineers, and scientists. Most of the material we present is available elsewhere, but is scattered throughout a variety of sources and occasionally buried in obscurity. Some of our results are original (or more likely, independent rediscoveries). We have included some material that we cannot honestly say is neces sary to understand modern economic theory, but may yet prove useful in future research.
