O.A. Malygina

Contents the integration principle of modern education technologies is given. This principle is one of the main statement which guarantees the training professional mobile competent specialists of high-tech disciplines. Integration of modern teaching technologies allows to eliminate defects and restrictions individual technologies, for example, the technology of module, contextual, problem and system activity-based teaching. Enriching each technology takes place through integration, it is extended opportunities of selection the optimal ways to achieve teaching purposes and control of teaching quality. The experimental model of studying higher mathematics is constructed in which the principle of integration modern education technologies is one of the leading principles. The realization of this principle in the course of study such higher mathematics sections as Fourier series, Fourier integral and transformation is described. Study of Fourier series, Fourier integral and transformation starts from investigation of applied problems which arise in professional activities of radio engineer, electrician and other specialists of high technology disciplines. The systems liable to study are fixed, for example, "function", "signal", "transformation of signal" and others. Correspondences between these systems take shape. It is shown that considering new object "the system with transformation" is very useful for solution investigative problems. This object is more complicated system relatively starting system. The notion of isomorphism for systems with transformation puts into operation. As an example of isomorphism for such objects is considered Fourier transformation. In the process of experimental education students obtain valuable mathematical and methodological knowledge and skills, base for successful learning support of special disciplines, creative fulfillment of term papers and graduation works. Future graduating students of technical universities obtain the base of professional mobility.