This is a free textbook on graduate-level applied math, treating topics like complex analysis, special functions, orthogonal polynomials, numerical methods in photonics, symmetry in photonics, dynamical systems, ...
It is used as a textbook in the course "Mathematics for Photonics" at Ghent University. Although some examples are drawn from the field of photonics, the material can be relevant for people in other fields of physics or engineering.
This textbook takes an 'active approach': rather than only providing explanations, at key points you are given hints and are explicitly asked to try and derive the next steps on your own. This is then followed by the explanation. Obviously, to get maximum benefit from this approach, it is imperative that you work through these steps yourselves. You should resist the temptation to immediately skip to the answer, as this will only result in the illusion of competence.
This textbook is supported by videos on the Active Math YouTube channel.
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