The relevance of the research is due to the fact that the study of further mathematics in an engineering university provides the level of general education and general cultural development of students, and educational background in special disciplines for the subsequent professional tasks solution. At the same time, there are significant difficulties in mastering the "Further Mathematics" course by students. In this regard, this work is aimed at solving the problem of improving the process of teaching further mathematics in an engineering university using a combination of project based learning and case study (project-case technology). It contributes to developing professional competencies of students of architectural and engineering specialties through the use of solving practice-oriented problems, which brings them closer to real future professional activities. The leading methods in the problem study were: entrance subject testing of the training level in mathematical; pedagogical observation during lessons where project based learning and case study were used; questionnaires upon completion of the "Further Mathematics" course, aimed at identifying both the level of mathematical maturity and the level of ability to conduct research activities necessary to solve non-standard professional tasks. Methods of mathematical statistics were used to process the experimental data. The main results of the study consist in highlighting the features of the combination of project based learning and case study when mastering the "Further Mathematics" course by students, future architect engineers. The significance of the obtained results lies in the fact that the proposed organization of the educational process can be implemented in various engineering specialties, considering a selection of specific professional case tasks.