The article is devoted to the problem of improving the quality of mathematical training for students of technical universities through the design and implementation of professionally oriented cases. The paper substantiates the need for a transition from traditional academic teaching of mathematical analysis and linear algebra and analytical geometry to practice-oriented learning using open educational resources. The methodology of case development is proposed, which includes four stages: the analysis of professional tasks, the selection and adaptation of open educational resources, the development of the case structure and its testing. The principles of selection of open resources (accessibility, license purity, methodological validity, adaptability) are described. Examples of professionally oriented cases for the training areas «Information Security», «Economics», «Engineering Mechanics» and «Construction» are given. The results of the pilot implementation of the developed cases in the educational process of the technical university are discussed. Special attention is paid to the didactic principles of case design, criteria for their effectiveness and methodological recommendations for teachers.