Generalized Gaussian Error Calculus PDF Download
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Author: Michael Grabe
Publisher: Springer Science & Business Media
ISBN: 3642033059
Category : Science
Languages : en
Pages : 298
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Book Description
This book addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. It integrates mathematics and its applications to physical measurements, and serves as a text for graduate students and a reference for researchers.
Author: Michael Grabe
Publisher: Springer Science & Business Media
ISBN: 3642033059
Category : Science
Languages : en
Pages : 298
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Book Description
This book addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. It integrates mathematics and its applications to physical measurements, and serves as a text for graduate students and a reference for researchers.
Author: Michael Grabe
Publisher: Springer
ISBN: 3319048880
Category : Technology & Engineering
Languages : en
Pages : 394
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Book Description
This book recasts the classical Gaussian error calculus from scratch, the inducements concerning both random and unknown systematic errors. The idea of this book is to create a formalism being fit to localize the true values of physical quantities considered – true with respect to the set of predefined physical units. Remarkably enough, the prevailingly practiced forms of error calculus do not feature this property which however proves in every respect, to be physically indispensable. The amended formalism, termed Generalized Gaussian Error Calculus by the author, treats unknown systematic errors as biases and brings random errors to bear via enhanced confidence intervals as laid down by Student. The significantly extended second edition thoroughly restructures and systematizes the text as a whole and illustrates the formalism by numerous numerical examples. They demonstrate the basic principles of how to understand uncertainties to localize the true values of measured values - a perspective decisive in view of the contested physical explorations.
Author: Michael Grabe
Publisher: Morgan & Claypool Publishers
ISBN: 1643270966
Category : Science
Languages : en
Pages : 81
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Book Description
Metrological data is known to be blurred by the imperfections of the measuring process. In retrospect, for about two centuries regular or constant errors were no focal point of experimental activities, only irregular or random error were. Today's notation of unknown systematic errors is in line with this. Confusingly enough, the worldwide practiced approach to belatedly admit those unknown systematic errors amounts to consider them as being random, too. This book discusses a new error concept dispensing with the common practice to randomize unknown systematic errors. Instead, unknown systematic errors will be treated as what they physically are- namely as constants being unknown with respect to magnitude and sign. The ideas considered in this book issue a proceeding steadily localizing the true values of the measurands and consequently traceability.
Author: Nicolas Bouleau
Publisher: Walter de Gruyter
ISBN: 3110180367
Category : Business & Economics
Languages : en
Pages : 244
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Book Description
The book deals with propagation of errors on data through mathematical models with applications in finance and physics. It is interesting for scientists and practitioners when studying the sensitivity of their models to small changes in the hypotheses. The book differs from what is usually done in sensitivity analysis because it yields powerful new tools allowing to manage errors in stochastic models as those used in modern finance.
Author: Martin H. Trauth
Publisher: Springer Nature
ISBN: 3030384411
Category : Science
Languages : en
Pages : 526
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Book Description
MATLAB® is used in a wide range of geoscientific applications, e.g. for image processing in remote sensing, for creating and processing digital elevation models, and for analyzing time series. This book introduces readers to MATLAB-based data analysis methods used in the geosciences, including basic statistics for univariate, bivariate and multivariate datasets, time-series analysis, signal processing, the analysis of spatial and directional data, and image analysis. The revised and updated Fifth Edition includes seven new sections, and the majority of the chapters have been rewritten and significantly expanded. New sections include error analysis, the problem of classical linear regression of log-transformed data, aligning stratigraphic sequences, the Normalized Difference Vegetation Index, Aitchison’s log-ratio transformation, graphical representation of spherical data, and statistics of spherical data. The book also includes numerous examples demonstrating how MATLAB can be used on datasets from the earth sciences. The supplementary electronic material (available online through SpringerLink) contains recipes that include all the MATLAB commands featured in the book and the sample data.
Author: Martin H. Trauth
Publisher: Springer Nature
ISBN: 3031077199
Category : Science
Languages : en
Pages : 463
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Book Description
Python is used in a wide range of geoscientific applications, such as in processing images for remote sensing, in generating and processing digital elevation models, and in analyzing time series. This book introduces methods of data analysis in the geosciences using Python that include basic statistics for univariate, bivariate, and multivariate data sets, time series analysis, and signal processing; the analysis of spatial and directional data; and image analysis. The text includes numerous examples that demonstrate how Python can be used on data sets from the earth sciences. The supplementary electronic material (available online through Springer Link) contains the example data as well as recipes that include all the Python commands featured in the book.
Author: Abdul Jerri
Publisher: CRC Press
ISBN: 1000147525
Category : Mathematics
Languages : en
Pages : 852
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Book Description
This reference/text desribes the basic elements of the integral, finite, and discrete transforms - emphasizing their use for solving boundary and initial value problems as well as facilitating the representations of signals and systems.;Proceeding to the final solution in the same setting of Fourier analysis without interruption, Integral and Discrete Transforms with Applications and Error Analysis: presents the background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem; discusses modelling of the basic partial differential equations, as well as the solutions in terms of the main special functions; considers the Laplace, Fourier, and Hankel transforms and their variations, offering a more logical continuation of the operational method; covers integral, discrete, and finite transforms and trigonometric Fourier and general orthogonal series expansion, providing an application to signal analysis and boundary-value problems; and examines the practical approximation of computing the resulting Fourier series or integral representation of the final solution and treats the errors incurred.;Containing many detailed examples and numerous end-of-chapter exercises of varying difficulty for each section with answers, Integral and Discrete Transforms with Applications and Error Analysis is a thorough reference for analysts; industrial and applied mathematicians; electrical, electronics, and other engineers; and physicists and an informative text for upper-level undergraduate and graduate students in these disciplines.
Author: Luis Manuel Braga de Costa Campos
Publisher: CRC Press
ISBN: 1420071157
Category : Mathematics
Languages : en
Pages : 888
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Book Description
Combining mathematical theory, physical principles, and engineering problems, Generalized Calculus with Applications to Matter and Forces examines generalized functions, including the Heaviside unit jump and the Dirac unit impulse and its derivatives of all orders, in one and several dimensions. The text introduces the two main approaches to generalized functions: (1) as a nonuniform limit of a family of ordinary functions, and (2) as a functional over a set of test functions from which properties are inherited. The second approach is developed more extensively to encompass multidimensional generalized functions whose arguments are ordinary functions of several variables. As part of a series of books for engineers and scientists exploring advanced mathematics, Generalized Calculus with Applications to Matter and Forces presents generalized functions from an applied point of view, tackling problem classes such as: Gauss and Stokes’ theorems in the differential geometry, tensor calculus, and theory of potential fields Self-adjoint and non-self-adjoint problems for linear differential equations and nonlinear problems with large deformations Multipolar expansions and Green’s functions for elastic strings and bars, potential and rotational flow, electro- and magnetostatics, and more This third volume in the series Mathematics and Physics for Science and Technology is designed to complete the theory of functions and its application to potential fields, relating generalized functions to broader follow-on topics like differential equations. Featuring step-by-step examples with interpretations of results and discussions of assumptions and their consequences, Generalized Calculus with Applications to Matter and Forces enables readers to construct mathematical–physical models suited to new observations or novel engineering devices.
Author: Alexander Altland
Publisher: Cambridge University Press
ISBN: 1108471226
Category : Mathematics
Languages : en
Pages : 723
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Book Description
Introduces fundamental concepts and computational methods of mathematics from the perspective of physicists.
Author: Nicolas Bouleau
Publisher: Springer Nature
ISBN: 3030885755
Category : Mathematics
Languages : en
Pages : 448
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Book Description
The Mathematics of Errors presents an original, rigorous and systematic approach to the calculus of errors, targeted at both the engineer and the mathematician. Starting from Gauss's original point of view, the book begins as an introduction suitable for graduate students, leading to recent developments in stochastic analysis and Malliavin calculus, including contributions by the author. Later chapters, aimed at a more mature audience, require some familiarity with stochastic calculus and Dirichlet forms. Sensitivity analysis, in particular, plays an important role in the book. Detailed applications in a range of fields, such as engineering, robotics, statistics, financial mathematics, climate science, or quantum mechanics are discussed through concrete examples. Throughout the book, error analysis is presented in a progressive manner, motivated by examples and appealing to the reader’s intuition. By formalizing the intuitive concept of error and richly illustrating its scope for application, this book provides readers with a blueprint to apply advanced mathematics in practical settings. As such, it will be of immediate interest to engineers and scientists, whilst providing mathematicians with an original presentation. Nicolas Bouleau has directed the mathematics center of the Ecole des Ponts ParisTech for more than ten years. He is known for his theory of error propagation in complex models. After a degree in engineering and architecture, he decided to pursue a career in mathematics under the influence of Laurent Schwartz. He has also written on the production of knowledge, sustainable economics and mathematical models in finance. Nicolas Bouleau is a recipient of the Prix Montyon from the French Academy of Sciences.
