A textbook for technical institutes devoted to special branches of mathematics: field theory, theory of analytic functions, operation calculus, linear algebra, tensors, calculus of variations, integral equations and additional questions of ordinary differential equations. The presentation is conducted from the standpoint of applied mathematics, special attention is paid to the quantitative description of facts. Individual chapters, and in some cases smaller sections, of the book can be read independently. The manual is addressed to students, graduate students, engineers, teachers and scientists specializing in the field of technical sciences.