Measuring and Modeling by Examples: How Mathematical Functions Can Be Used (and Misused) to Describe the World

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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.