This is an entertaining book which comprises a variety of mathematical problems, mostly related to calculations, and addressed to students in a undergraduate level in either Mathematics, Physics or Engineering degrees. The common argumentative line of all topics in the book is the use of Matlab programs which solve or simulate the problems at hand.
The main topics included are:
- The study of the Laplace equation in a region in the plane, mainly through the problem of finding the temperature of a plate given the distribution of temperatures of the border. This is solved via Fourier analysis, by discretizing, and also by a Monte-Carlo technique.
- Some problems on dynamical mechanical systems, mostly the study of several configurations of hanging masses (with hooks), studying how the systems develop and issues related to periodicity.
- The three-body problem, studying the stability of the system starting from different configurations, and giving a theoretical analysis and also numerical simulations. This chapter includes nice historical remarks on the problem.
- Analysis of electric circuits, with a theoretical analysis, and also using computer simulations of circuits.
Some other fun problems are included in the book, most of them aimed to show how computers may help in finding or guessing a solution. Also several fictiional stories appear scattered along the book. Finally, each chapter includes a collection of challenge problems for the interested reader (with solutions appearing at the end of the book).
Altogether, this is a brain stimulating read, recommended for a general audience of mathematically minded people with interest in physics or in the use or programming to solve mathematical problems.