An Introduction to Error Analysis

The Study of Uncertainties in Physical Measurements

Author: John Robert Taylor

Publisher: Sterling Publishing Company

ISBN: 9780935702750

Category: Mathematics

Page: 327

View: 9390

The need for error analysis is captured in the book's arresting cover shot - of the 1895 Paris train disaster. The early chapters teach elementary techniques of error propagation and statistical analysis to enable students to produce successful lab reports. Later chapters treat a number of more advanced mathematical topics, with many examples from mechanics and optics. End-of-chapter problems include many that call for use of calculators or computers, and numerous figures help readers visualise uncertainties using error bars.

An Introduction to Error Analysis

The Study of Uncertainties in Physical Measurements

Author: John Robert Taylor

Publisher: Univ Science Books

ISBN: 9780935702422

Category: Mathematics

Page: 327

View: 2576

Problems after each chapter

An Introduction to the Concept of Error Analysis

Author: Robert Wetzorke

Publisher: GRIN Verlag

ISBN: 3640506073

Category:

Page: 28

View: 1198

Seminar paper from the year 2005 in the subject English - Pedagogy, Didactics, Literature Studies, grade: 1,3, Technical University of Braunschweig (Englisches Seminar), language: English, abstract: Foreign Language Pedagogy (FLP), in general, aims to convey to teachers the essential information about the role of the learner and the teacher in the process of language learning, and also provides them with theoretical, didactic methods and practical means for the foreign language classroom (FLC). We can even go a step further by claiming that the mission of FLP is to research for and establish the supreme way of a teaching a foreign language (FL) to the learners. However, within this field of research it becomes quite obvious that the learners take in a rather passive role and do not contribute very much to new research data and, hence, new approaches towards foreign language teaching (FLT). This thesis can be held true, to give just one example, when we consider the various teaching methods for the FLC. Although the role of the learner is taken into account in each method, the learners are fairly more than "testing objects" of teaching models hypothesized by didactic scientists. On the other hand, one must admit that in correspondence with the recent emergence and establishment of the communicative approach (CA), the learners preferences and demands have been taken far more into consideration and their linguistic and communicative performance serve as source for methodological research input and constructive, teacher strategies-oriented as well as learner strategies-oriented output offered by science. Recently, and paradoxically enough, it can be perceived intensive discussion concerning the question how to deal best with errors produced by learners. More precisely, there has been a shift from the formerly applied "Contrastive Analysis" (CAH) toward the occupation with "Error Analysis" (EA). (...)

Measurements and Their Uncertainties

A Practical Guide to Modern Error Analysis

Author: Ifan Hughes,Thomas Hase

Publisher: Oxford University Press

ISBN: 0199566321

Category: Mathematics

Page: 136

View: 7674

This short book is primarily intended to be used in undergraduate laboratories in the physical sciences. No prior knowledge of statistics is assumed, with the necessary concepts introduced where needed, and illustrated graphically. In contrast to traditional treatments a combination of spreadsheet and calculus-based approaches is used. Error analysis is introduced at a level accessible to school leavers, and carried through to research level. The emphasisthroughout is on practical strategies to be adopted in the laboratory. Error calculation and propagation is presented though a series of rules-of-thumb, look-up tables and approaches amenable to computeranalysis.

Data Reduction and Error Analysis for the Physical Sciences

Author: Philip R. Bevington,D. Keith Robinson

Publisher: N.A

ISBN: 9780071199261

Category: Data reduction

Page: 320

View: 3856

The purpose of this book is to provide an introduction to the concepts of statistical analysis of data for students at the undergraduate and graduate level, and to provide tools for data reduction and error analysis commonly required in the physical sciences. The presentation is developed from a practical point of view, including enough derivation to justify the results, but emphasizing methods of handling data more than theory. The text provides a variety of numerical and graphical techniques. Computer programs that support these techniques will be available on an accompanying website in both Fortran and C++.

200 Puzzling Physics Problems

With Hints and Solutions

Author: P. Gnädig,G. Honyek,K. F. Riley

Publisher: Cambridge University Press

ISBN: 9780521774802

Category: Science

Page: 257

View: 5498

This book contains instructive, challenging and fun physics problems for students at all levels.

A Graduate Introduction to Numerical Methods

From the Viewpoint of Backward Error Analysis

Author: Robert Corless,Nicolas Fillion

Publisher: Springer Science & Business Media

ISBN: 1461484537

Category: Mathematics

Page: 869

View: 1667

This book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations. The book contains detailed illustrations, chapter summaries and a variety of exercises as well some Matlab codes provided online as supplementary material. “I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine A Graduate Introduction to Numerical Methods and Backward Error Analysis” has been selected by Computing Reviews as a notable book in computing in 2013. Computing Reviews Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.

Finite Elements

An Introduction to the Method and Error Estimation

Author: Ivo Babuska,John Whiteman,Theofanis Strouboulis

Publisher: Oxford University Press

ISBN: 0198506694

Category: Mathematics

Page: 323

View: 478

Computational modelling is the process of representing some activity, for example a physical happening, first by a mathematical model and then of solving the model using a numerical technique such as the finite element method. Both parts of this process involve approximations. As a result error estimation has to be employed to assess the reliability of the computational modelling process. This book addresses the verification of the numerical methods, in thiscase finite elements methods, involved in the process, by analysing the finite element errors. The unique feature of the book is that it brings together both theoretical error analysis and the computed solutions, highlighting their interplay.

Finite Element Analysis with Error Estimators

An Introduction to the FEM and Adaptive Error Analysis for Engineering Students

Author: J. E. Akin

Publisher: Elsevier

ISBN: 9780080472751

Category: Technology & Engineering

Page: 512

View: 4167

This key text is written for senior undergraduate and graduate engineering students. It delivers a complete introduction to finite element methods and to automatic adaptation (error estimation) that will enable students to understand and use FEA as a true engineering tool. It has been specifically developed to be accessible to non-mathematics students and provides the only complete text for FEA with error estimators for non-mathematicians. Error estimation is taught on nearly half of all FEM courses for engineers at senior undergraduate and postgraduate level; no other existing textbook for this market covers this topic. The only introductory FEA text with error estimation for students of engineering, scientific computing and applied mathematics Includes source code for creating and proving FEA error estimators

An Introduction to Uncertainty in Measurement

Using the GUM (Guide to the Expression of Uncertainty in Measurement)

Author: L. Kirkup,R. B. Frenkel

Publisher: Cambridge University Press

ISBN: 1139454900

Category: Science

Page: 233

View: 4021

Measurement shapes scientific theories, characterises improvements in manufacturing processes and promotes efficient commerce. In concert with measurement is uncertainty, and students in science and engineering need to identify and quantify uncertainties in the measurements they make. This book introduces measurement and uncertainty to second and third year students of science and engineering. Its approach relies on the internationally recognised and recommended guidelines for calculating and expressing uncertainty (known by the acronym GUM). The statistics underpinning the methods are considered and worked examples and exercises are spread throughout the text. Detailed case studies based on typical undergraduate experiments are included to reinforce the principles described in the book. This guide is also useful to professionals in industry who are expected to know the contemporary methods in this increasingly important area. Additional online resources are available to support the book at www.cambridge.org/9780521605793.

An Introduction to Applied Matrix Analysis

Author: Xiao Qing Jin,Seak-Weng Vong

Publisher: World Scientific Publishing Company

ISBN: 9814749486

Category: Mathematics

Page: 144

View: 8269

It is well known that most problems in science and engineering eventually progress into matrix problems. This book gives an elementary introduction to applied matrix theory and it also includes some new results obtained in recent years. The book consists of eight chapters. It includes perturbation and error analysis; the conjugate gradient method for solving linear systems; preconditioning techniques; and least squares algorithms based on orthogonal transformations, etc. The last two chapters include some latest development in the area. In Chap. 7, we construct optimal preconditioners for functions of matrices. More precisely, let f be a function of matrices. Given a matrix A, there are two choices of constructing optimal preconditioners for f(A). Properties of these preconditioners are studied for different functions. In Chap. 8, we study the Bottcher–Wenzel conjecture and discuss related problems. This is a textbook for senior undergraduate or junior graduate students majoring in science and engineering. The material is accessible to students who, in various disciplines, have basic linear algebra, calculus, numerical analysis, and computing knowledge. The book is also useful to researchers in computational science who are interested in applied matrix theory.

Classical Mechanics

Author: John Robert Taylor

Publisher: University Science Books

ISBN: 9781891389221

Category: Science

Page: 786

View: 1692

'Classical Mechanics' is intended for students who have studied some mechanics in an introductory physics course. A particular highlight is the chapter on chaos, which focuses on a few simple systems to give truly comprehensible coverage.

An Introduction to Intelligence Research and Analysis

Author: Jerome Clauser

Publisher: Scarecrow Press

ISBN: 9780810861817

Category: Political Science

Page: 219

View: 1278

First published in the 1970s by Jerome Clauser, this book was used by intelligence analysts to track and monitor the Communist threat. Although today's environment has changed considerably, analysts still need to understand the basics. The book focuses on how to research, what qualities are needed to be an intelligence analyst, and what methods can be used.

An Introduction to Statistical Learning

with Applications in R

Author: Gareth James,Daniela Witten,Trevor Hastie,Robert Tibshirani

Publisher: Springer Science & Business Media

ISBN: 1461471389

Category: Mathematics

Page: 426

View: 1900

An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, and more. Color graphics and real-world examples are used to illustrate the methods presented. Since the goal of this textbook is to facilitate the use of these statistical learning techniques by practitioners in science, industry, and other fields, each chapter contains a tutorial on implementing the analyses and methods presented in R, an extremely popular open source statistical software platform. Two of the authors co-wrote The Elements of Statistical Learning (Hastie, Tibshirani and Friedman, 2nd edition 2009), a popular reference book for statistics and machine learning researchers. An Introduction to Statistical Learning covers many of the same topics, but at a level accessible to a much broader audience. This book is targeted at statisticians and non-statisticians alike who wish to use cutting-edge statistical learning techniques to analyze their data. The text assumes only a previous course in linear regression and no knowledge of matrix algebra.

An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems

Author: Luis Tenorio

Publisher: SIAM

ISBN: 1611974925

Category: Mathematics

Page: 269

View: 7332

Inverse problems are found in many applications, such as medical imaging, engineering, astronomy, and geophysics, among others. To solve an inverse problem is to recover an object from noisy, usually indirect observations. Solutions to inverse problems are subject to many potential sources of error introduced by approximate mathematical models, regularization methods, numerical approximations for efficient computations, noisy data, and limitations in the number of observations; thus it is important to include an assessment of the uncertainties as part of the solution. Such assessment is interdisciplinary by nature, as it requires, in addition to knowledge of the particular application, methods from applied mathematics, probability, and statistics. This book bridges applied mathematics and statistics by providing a basic introduction to probability and statistics for uncertainty quantification in the context of inverse problems, as well as an introduction to statistical regularization of inverse problems. The author covers basic statistical inference, introduces the framework of ill-posed inverse problems, and explains statistical questions that arise in their applications. An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems÷includes many examples that explain techniques which are useful to address general problems arising in uncertainty quantification, Bayesian and non-Bayesian statistical methods and discussions of their complementary roles, and analysis of a real data set to illustrate the methodology covered throughout the book.

A Student's Guide to Data and Error Analysis

Author: Herman J. C. Berendsen

Publisher: Cambridge University Press

ISBN: 1139497855

Category: Technology & Engineering

Page: N.A

View: 2368

All students taking laboratory courses within the physical sciences and engineering will benefit from this book, whilst researchers will find it an invaluable reference. This concise, practical guide brings the reader up-to-speed on the proper handling and presentation of scientific data and its inaccuracies. It covers all the vital topics with practical guidelines, computer programs (in Python), and recipes for handling experimental errors and reporting experimental data. In addition to the essentials, it also provides further background material for advanced readers who want to understand how the methods work. Plenty of examples, exercises and solutions are provided to aid and test understanding, whilst useful data, tables and formulas are compiled in a handy section for easy reference.

An Introduction to Numerical Analysis

Author: Endre Süli,David F. Mayers

Publisher: Cambridge University Press

ISBN: 1139437887

Category: Mathematics

Page: N.A

View: 8937

Numerical analysis provides the theoretical foundation for the numerical algorithms we rely on to solve a multitude of computational problems in science. Based on a successful course at Oxford University, this book covers a wide range of such problems ranging from the approximation of functions and integrals to the approximate solution of algebraic, transcendental, differential and integral equations. Throughout the book, particular attention is paid to the essential qualities of a numerical algorithm - stability, accuracy, reliability and efficiency. The authors go further than simply providing recipes for solving computational problems. They carefully analyse the reasons why methods might fail to give accurate answers, or why one method might return an answer in seconds while another would take billions of years. This book is ideal as a text for students in the second year of a university mathematics course. It combines practicality regarding applications with consistently high standards of rigour.

The Analysis of Physical Measurements

Author: Emerson M. Pugh,George Harvey Winslow

Publisher: N.A

ISBN: N.A

Category: Physical measurements

Page: 246

View: 6468

An Introduction to Interaction

Understanding Talk in Formal and Informal Settings

Author: Angela Cora Garcia

Publisher: A&C Black

ISBN: 1623561523

Category: Language Arts & Disciplines

Page: 288

View: 6577

This textbook provides an in-depth introduction to the theoretical perspectives and methods of doing conversation analysis, an approach to the study of talk in interaction which grew out of the work of Garfinkel, Sacks, Schegloff, and Jefferson. This book is unique in that it provides comprehensive instruction in both interaction in ordinary conversations in everyday life as well as talk in institutional settings and a wide range of workplace and business interactions, while teaching both major research findings and how to conduct conversation analytic research. The book is designed to be useful for students of linguistics, sociology, and communication studies, and is written in clear and accessible prose. The Companion Website provides additional resources for instructors, such as questions and data excerpts for tests and in class exercises, audio and video clips for transcription practice, and guides for instructors on a range of topics covered in the course.