The study proposes a diagnostic control method for assessing the quality of commercial batches of hydraulic oils based on the kinetics of changes in the thickness of lubricating layers, shear stresses of the lubricating material, and effective viscosity in tribotechnical contact. Timely and high-quality tribomonitoring of lubricants provides a perspective on their rational use and reduced wear of equipment parts. The developed methodology simulates the operation of gears in rolling conditions with a slip of 30% using a roller analogy. Samples of AMG-10 oil from two manufacturers were analyzed. For "Bora B" AMG-10 oil (sample 1) with gradients of the sliding speed of the lubricating layer in contact from 5.63·103 to 5.73·105 с-1, the effective viscosity is set at the level of 4249 and 5039 Pa·s at a bulk oil temperature of 20 and 100 oС, respectively, which indicates the resistance of oil components to destruction under conditions of increasing shear rate gradient. For AMG-10 oil (sample 2), the effective contact viscosity decreases by 1.53 times both at an oil temperature of 20 oС and at 100 oС and is 2764 Pa·s (at 20 oС) and 3309 Pa·s (at 100 oС), which indicates the destruction of the components of the lubricant. For "Bora B" AMG-10 oil, effective lubricating properties have been established both during the start-up period and at maximum revolutions in conditions of rolling with slipping. It was shown that at start-up, regardless of the temperature of the lubricant, the mixed lubrication mode dominates. At the maximum revolutions of the tested samples, the hydrodynamic lubrication mode dominates, which indicates the effective lubricating properties of the Bora B AMG-10 oil. According to the kinetics of changes in the rheological parameters of oils, it was established that the resistance of the lubricant's components to mechano-thermal destruction under non-stationary lubrication conditions contributes to the effective formation of a lubricating layer in contact with a high bearing capacity

The significance of the material presented in the article is due to the necessity of developing and implementing the latest information technologies at the study of higher mathematics using the systems of computer mathematics. The solution of the standard tasks of higher mathematics on the topic of differential equations involves the execution of bulky, similar arithmetic calculations and records. If there is an error in the calculation, its localization takes a lot of time, which leads to the student's quick fatigue. The concept of adaptation of SCM Maple to higher mathematics is suggested by creating a training Maple simulator on the topic "Linear homogeneous differential equations" in order to more effectively master students 'material, as well as to enhance students' learning and cognitive activity. The main results of the authors are presented in the field of development of the educational complex in higher mathematics, the main element of which are procedural simulators as well as procedure generators.