MEASURING AND MODELING BY EXAMPLES

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This book starts with an anthology of mathematical functions that can be useful to describe phenomena that occur in the world we see, and how their features can be adjusted by changing their parameters. Then we have a look at the art of measuring and quantifying the world, and how to do this most efficiently and precisely. The most important part is about finding the "pattern" in the measurements: a mathematical function that "fits" with the data. This can be chosen according to several criteria, and using different algorithms, for example the new "multidirectional least squares regression". The last part shows many real life examples in various fields of science: experiments and their analyses. Request Inspection Copy Sample Chapter(s) Preface Introduction Contents: About the Author Preface Introduction Some Useful Functions to Describe the World: Functions and Their Linear Transformations Polynomials Power Functions Homographic Functions Other Rational Functions Exponential Functions Logarithmic Functions Sigmoid-Like Functions Peak-Shaped Functions Periodic and Semiperiodic Functions Miscellaneous Functions Harvesting Data: Measurement Uncertainties Resolution Versus Accuracy "Difficult" Quantities Disturbance by Measurements Error Propagation Minimizing Errors Finding the Pattern: Some Rudimentary Tools Regression Analysis — What is It? Going Toward the Best Fit Regression Analysis — Use It Wisely Judging the Model Case Studies: Physics, Chemistry, Engineering Geography, Climate etc. Life Sciences Psychology etc. Economy etc. Index Readership: High school and college students who has the basics of calculus and statistics. Teachers and researchers who need inspiration and a new view on some old problems. Engineers and anyone who needs models for prediction, calibration and hypothesis testing.