Although the book is parochial, given its authors are all Finnish and the original language in print was Finnish (although this version is the English translation), the text has many topics that are universal in nature and can be profitable for professional or aspiring engineers. Mathematical modelling is a product of several different contributors, all from Finnish universities. The result is a text used by over 2,000 students.

Chapter 1 deals with the fundamentals of the modeling process. It is introductory in nature and concentrates on necessary definitions. Chapter 2 is very well done. It discusses mathematical models and their applications in several different fields of science, business, and social studies. Chapter 3 increases in sophistication by covering the use of modeling with different kinds of systems, for example, discrete and dynamic (stochastic). Chapters 4 and 5 deal with integer models and data-based models, respectively. Chapter 5 is the first chapter containing practice exercises for the student. The problems are practical in nature, yet require the application of classical techniques in modeling. Chapter 6 is exceptionally interesting to the professional or aspiring engineer because it focuses on “soft computing methods,” that is, challenges involving fuzzy variables. The treatment is advanced and yet the authors are careful to explain every principle they utilize.

Chapter 7 covers dimensional analysis. The coverage is classic, standard, and thorough. Chapter 8 deals with modeling with differential equations, whereas chapter 9 concentrates on continuum models. Chapter 10 explains techniques for model simplification. The reader who is a statistician will be immediately reminded of how the techniques presented in the chapter mirror those of multivariate statistical applications in regression. Chapter 11 is exclusively devoted to the use of modeling in acoustical phenomena, whereas chapter 12 covers inverse problems

The book concludes with a wonderful chapter presenting different challenges that can be solved using modeling by the gifted mathematics or engineering student. For example:

A common spring-mass combination makes up an oscillator with the well-known physical model. Now assume that the spring constant as well as the matter that causes the dampening are known only vaguely, i.e., as fuzzy numbers. What can be said about the oscillator’s movement?

This is only one example of a plethora of fascinating problems and assignments that could be made available to students.

This is an excellent book, written with a myriad of interesting and very practical problems and applications. The contributors to the text are obviously scientific scholars who are elegantly educated.