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This book provides a thorough introduction to thechallenge of applying mathematics in real-world scenarios. Modelling tasksrarely involve well-defined categories, and they often requiremultidisciplinary input from mathematics, physics, computer sciences, orengineering. In keeping with this spirit of modelling, the book includes awealth of cross-references between the chapters and frequently points to thereal-world context.The book combines classical approaches to modellingwith novel areas such as soft computing methods, inverse problems, and modeluncertainty. Attention is also paid to the interaction between models, data andthe use of mathematical software. The reader will find a broad selection oftheoretical tools for practicing industrial mathematics, including the analysisof continuum models, probabilistic and discrete phenomena, and asymptotic andsensitivity analysis.