The aim of this book is twofold: to develop some standard models of physical and biological processes (the transport equation, heat conduction, the beam equation, fluid dynamics and structured population models) in mathematical language; and, probably more importantly, to show how and why to design concrete engineering experiments for comparing numerical results of models with specific experimental data. It is necessary to find adequate values of coefficients to do such a comparison. For these purposes, the book contains chapters on statistical aspects of inverse problems and on feedback control systems. A basic calculus course is sufficient for understanding the mathematics used in the text. The book can be recommended to advanced undergraduate students, for whom mathematics is a bit more than just proving theorems. Teachers can also find suggestions of motivations for introductory parts of lectures on ordinary differential equations and partial differential equations.