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.
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.
Koen Van de moortel, 8 April 1962, Antwerpen, Belgium. MSc. experimental physics (Universities of Antwerp & Ghent, Belgium). Independent math, & physics tutor, Delphi Pascal programmer, photographer, author of books and teaching texts about math, physics, scientific methodology ... (in Dutch), organizer of many lectures & debates about special and controversial scientific topics.
