Heritage Fourier and problems of modernization of the course of mathematical analysis for physicists

Fourier lived and worked in an era when, in the studies on mathematical analysis, the first, heroic period and began a long period of ordering, improvement and strict presentation initial ideas. During this period, new and wonderful ideas were formulated, but the spirit of the era defined The form and style of the presentation of those classical textbooks on mathematical analysis, according to which we now teach students. In the modern era, classical mathematics increasingly interacts with the mathematics of the computer age. This forces us to introduce new elements into seemingly well-established sections of mathematical analysis