This paper considers the problem of modeling how objectives are set by a human being. We find this problem interesting mainly in context of the research of so-called goal-pursuing systems, which include: enterprises, schools, military troops, administrative regions, manned aircraft etc. An inherent element of such systems is a human being, who performs a function of setting objectives. The reason that underlies setting objectives is emotional experience. It is also connected with motivation of activity in the process of achieving objectives. It is emotional experience that changes one’s initial state of spirit into aim and motive.

To start a procedure of formulating goal there must be a requirement and opportunity to satisfy it. This state creates disharmony between something objectively essential (but absent) and current condition of the body. Structure, which satisfies the requirement is called the impulse. After finding the impulse and under the influence of emotion, requirement tranforms into motive and impulse - into goal.

The emotional experience model was formulated as a Cauchy's task for a system of differential equations. The solution allowed for drawing the emotional intensity curve and specifying its fundamental characteristics: the beginning of emotion, the moment and height of emotional "peak" as well as points of changes in the nature of the course of emotion, and others. The solution allows for drawing the following conclusions.

1.The biggest importance of emotions’ intensity reaches later as there is a bigger initial range between the pragmatic information whose possession guarantees the need’s satisfaction and an actually existing level of pragmatic information which  an individual has at the actual time. 2. An emotional elevation created once does not “fall half asleep”. Gradualy decreasing the intensity, the emotion does not die but stays in an individual’s subconsciousness forever. 3. There is a doorstep of affection for perceiving emotions. 4. A fast rise of pragmatic information increases the level of the emotional tension. An ability of a fast processing information shows an individual’s intellect: the biggest individual’s intelligence is, the better this ability is developed. It means that the people who are more intelligent are “less emotional.”, their emotional experience is not that strong and does not last long like in case of the other people.

The results of the research opened the way for applying mathematics in studying other psychological phenomenons which leads to creating and developing mathematical psychology.

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