Van de Moortel K. Measuring and Modeling by Examples...2024

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Van de Moortel K. Measuring and Modeling by Examples...2024

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Textbook in PDF format This book starts with an anthology of mathematical functions (Polynomials, Power Functions, Other Rational Functions, Homographic Functions, Exponential Functions, Logarithmic Functions, Sigmoid-like Functions, Peak-Shaped Functions, Periodic and Semiperiodic Functions, Miscellaneous 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. From the preface: The book has four parts: (1) If you are not very familiar with the wide spectrum of those formulas, no problem. I take you on a journey in the world of mathematical functions first, well... at least some relatively simple and interesting kinds, and I’ll discuss their useful features. (2) Then I tell you some stories about the art of measuring. How to handle the uncertainties that are present in most data collections ? And how to avoid or minimize them as much as possible ? How to stick a number to observations that are not so easy to quantify, like “happiness”, or “wine quality” ? Some tricks and plain common sense can help you here! (3) Next, I try to clarify the process of finding the “best” possible function to use as a model for your observations. I also focus on some issues that are often neglected in this process, even by seasoned scholars, and introduce my improvements to existing techniques which I implemented in a software program “FittingKVdm”. Questions like “How trustworthy is my model ?” need to be asked certainly. (4) The last part of this book consists of many examples from the real world, from physics to psychology, from biology to linguistics, from sports to economy. In some of them, I analyze easy-to-repeat experiments that can be done at home or in a classroom, while others use data from public sources