Unique textbook makes the students understand differential equations

Nail Ibragimov, professor at BTH, has published a textbook that is unique in its way of teaching differential equations for undergraduate and graduate students. The textbook is translated into several languages and is used all over the world.

The book “A practical course in differential equations and mathematical modeling” from 2006 is used for his lectures on “Differential equations with Lie group analysis” and several related courses at BTH. The lectures are well-attended and above all – the students quickly learn the important area of differential equations. “For the first time I understand differential equations” was a statement from a students’ evaluation, Nail says proudly.

What is it that makes Nail’s book so unique and successful when it comes to learning? Well, the book combines ordinary and partial differential equations with the Norwegian mathematician Sophus Lie´s theories in group analysis. This has not been done before. Furthermore, the methods described in the book have many applications to mathematical models and it prepares students to solve modern problems in engineering and natural sciences but also in other areas e.g. you can predict cancer growth using these methods.

The book became a success and it has been translated into Swedish (2009), Chinese (2010), Russian (2012) and recently also appeared in German (2018). It is used by students, teachers and researchers worldwide.

Today, Nail Ibragimov is Professor Emeritus at the Department of Mathematics and Natural Sciences at BTH. He is extremely active in research on mathematical modeling of real world problems using Lie group analysis.

Now the course on differential equations at BTH, based on Nail’s book, is delivered by Dr. Raisa Khamitova for the students at the Master of Science in Mechanical Engineering programmes and exchange students. The original English version and its Swedish and Chinese translations are used by students in this course. In future the exchange students from Germany can use the German translation.

Nail is passionate and enthusiastic about disseminating knowledge about differential equations with Lie group analysis and their use in mathematical modelling. Recently, he developed, in the framework of the collaboration agreement between BTH and the Ufa Aviation Technical University (Russia), a Massive Open Online Course (MOOC) based on his book. The attendants from Russia used the Russian translation of the textbook. The course has been followed by about 600 students all over the world.


Nail Ibragimov is widely regarded as one of the world´s foremost experts in the field of differential equations, group analysis and mathematical modelling.

21 February 2018