In computer simulation of the learning process is usually assumed that all elements of the training material are assimilated equally durable. But in practice, the knowledge, which a student uses in its operations, are remembered much better. For a more precise study of didactic systems the multi component model of learning are proposed. It takes into account: 1) the transition of weak knowledge in trustworthy knowledge; 2) the difference in the rate of forgetting the trustworthy and weak knowledge. It is assumed that the rate of increase of student's knowledge is proportional to: 1) the difference between the level of the requirements of teachers and the number of learned knowledge; 2) the amount of learned knowledge, raised to some power. Examples of the use of a multi component model for the study of situations in the learning process are considered, the resulting graphs of the student's level of knowledge of the time are presented. A generalized model of learning, which allows to take into account the complexity of the various elements of the educational material are proposed. The possibility of creating a training program for the training of students of pedagogical institutes are considered.