Usual laying out of multivariable integral calculus in courses of analysis for engineers for technical universities, as a rule, doesn’t use the theory of exterior differential forms. It is shown here, that the introduction of basis of this theory into the course of analysis for engineers is very desirable. The pluses of this theory are shown, primarily extremely bigger algorithmic possibilities for formal calculating, comparing with present laying out of the the basis of this theory to the students of physical-technical engineering, electrical engineering, and thermal engineering professions seems very convenient. They use line integrals, surface integrals and vector analysis in the work (Maxwell’s equations, thermodynamic cycles etc). The importance of this theory at introduction into the teaching at technical universities of elements of differential geometry and topology, more extensive telling of the theory of differential equations or the complex analysis seems all the more important.