A First Course in Dimensional Analysis

A First Course in Dimensional Analysis
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.

A Student's Guide to Dimensional Analysis

A Student's Guide to Dimensional Analysis
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.

Dimensional Analysis

Dimensional Analysis
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.

Dimensional Analysis

Dimensional Analysis
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.

Applied Dimensional Analysis and Modeling

Applied Dimensional Analysis and Modeling
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

An Introduction to Infinite-Dimensional Analysis

An Introduction to Infinite-Dimensional Analysis
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.

Data Theory and Dimensional Analysis

Data Theory and Dimensional Analysis
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

Dimensional Analysis for Engineers

Dimensional Analysis for Engineers
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.

High-Dimensional Data Analysis with Low-Dimensional Models

High-Dimensional Data Analysis with Low-Dimensional Models
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.