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(s): Michael Grabe (auth.)
Edition: 2
Publisher: Springer International Publishing
Year: 2014
Language: English
Pages: 401
Tags: Measurement Science and Instrumentation; Appl.Mathematics/Computational Methods of Engineering; Mathematical Methods in Physics
Front Matter....Pages I-XIV
Front Matter....Pages 1-1
Basic Ideas of Measurement....Pages 3-15
Formalization of Measuring Processes....Pages 17-27
Normal Parent Distributions....Pages 29-52
Estimators and Expectations....Pages 53-66
Bias and Randomness....Pages 67-80
Error Propagation, Two Variables....Pages 81-96
Error Propagation, m Variables....Pages 97-104
Concatenated Functions....Pages 105-109
Front Matter....Pages 111-111
Least Squares Formalism....Pages 113-121
Consequences of Systematic Errors....Pages 123-133
Uncertainties of Least Squares Estimators....Pages 135-151
Uncertainty Spaces....Pages 153-170
Front Matter....Pages 171-171
Straight Lines....Pages 173-202
Exponentials....Pages 203-216
Planes....Pages 217-244
Circles....Pages 245-264
Parabolas....Pages 265-298
Least Squares Trigonometric Polynomials....Pages 299-307
Front Matter....Pages 309-309
Dissemination of Units....Pages 311-322
Calibration Chains....Pages 323-328
Front Matter....Pages 309-309
Pairwise Comparisons....Pages 329-335
Fundamental Constants of Physics....Pages 337-347
Essence of Metrology....Pages 349-349
Back Matter....Pages 351-401
