These lecture notes by very authoritative scientists survey recent advances of mathematics driven by industrial application showing not only how mathematics is applied to industry but also how mathematics has drawn benefit from interaction with real-word problems.
The famous David Report underlines that innovative high technology depends crucially for its development on innovation in mathematics. The speakers include three recent presidents of ECMI, one of ECCOMAS (in Europe) and the president of SIAM.

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Trees and paths: graph optimisation problems with industrial applications.- Mathematical models for polymer crystallization processes.- Differential equations in technology and medicine: Computational concepts, adaptive algorithms, and virtual labs.- Inverse problems and their regularization.- Aerodynamic shape optimization techniques based on control theory.- Complexity in industrial problems some remarks.- Flow and heat transfer in pressing of glass products.- Drag reduction by active control for flow past cylinders.- Signal processing for everyone.