Generalized Gaussian Error Calculus

Book Details

• Author: Michael Grabe

• Brand: Springer

• Edition: Illustrated

• Binding: Hardcover

• Number of Pages: 301

• Release Date: 26-02-2010

• ISBN: 9783642033049

• Package Dimensions: 9.2 x 6.1 x 0.9 inches

• Languages: English

About the Book

"Gaussian Error Calculus and Its Applications to Physical Measurements" by Michael Grabe is a meticulously revised and self-consistent exploration of the classical Gaussian error calculus. This book provides an integrated understanding of both mathematics and its practical applications to physical measurements, making it an essential text for graduate students and a valuable reference for researchers in the field.

Grabe’s work expands on the traditional Gaussian error calculus, which has long been used to handle random errors. The book addresses an important limitation of this classical method — the failure to distinguish between the true value of a measurand and the expectation of its estimator. Through detailed discussions, the author introduces the concept of traceability, which seeks to ensure that the true values of physical quantities in a measurement process are identified with specified measurement uncertainties.

The author also tackles systematic errors, which are unknown time-constant quantities that could not be quantified through traditional Gaussian methods. These errors are explored through intervals of estimated lengths, building on Gauss's own discussions of systematic errors. Grabe highlights the challenges metrologists face in accounting for and eliminating these errors in measurements.

This illustrated edition also includes biographical notes and references, making it not just a technical treatise but also a historical and theoretical study that blends practical insights with advanced mathematical models.

Key Features:

• Complete and self-consistent revision of the classical Gaussian error calculus

• Integrates mathematics with practical applications to physical measurements

• Focus on the concept of traceability and how it relates to the true values and uncertainties in measurements

• In-depth treatment of unknown systematic errors and their effect on physical measurements

• Essential for graduate students in metrology, physics, and engineering

• Provides a rigorous approach to understanding error analysis and measurement uncertainty

• Illustrated edition for better understanding of complex concepts

This book is a highly valuable resource for anyone engaged in metrology, measurement science, or any field where precision and accurate error analysis are paramount.