Department of Applied Mathematics was founded in 1963. From 1963 to 1988 it was headed by Doctor of Technical Sciences Professor N. P. Fleishman. Since 1988 the Head of the Department is Doctor of Science, Professor, Distinguished Professor of Ivan Franko National University of Lviv, Honored Worker of Education of Ukraine Ya. H. Savula. The Department formed a scientific field of problems of mathematical and computer modeling and optimization of physical – mechanical fields in solid environment. This research area is based on the scientific achievements of professors N. P. Fleyshman and Ya. H. Savula and their students. The modern period of Departments functionality under Professor Ya. H. Savula direction studies characterized variation- projection methods, finite and boundary elements and their application to the analysis and optimal management of physical – mechanical fields. Scientific work is being held on the Department in the field of numerical modeling of solutions of applied problems of different nature from heterogeneous mathematical models and using hybrid schemes of finite and boundary elements methods, in the numerical analysis of nonlinear problems of mathematical physics with application to shell theory, the theory of plasticity and to modeling of transport processes plasma. Scientific researches are focused on their use in science, technology and use for modeling in ecology and medicine.

Students and teachers of the Department participate in international grants and projects.
The Department maintains contacts with the Institutes of the National Academy of Sciences of Ukraine, with Ukraine and foreign universities.