This course is designed as a textbook for engineering students. It embraces the topics in mathematical analysis usually included into curricula of technical colleges. The course also contains some optional material which may be omitted in a first reading of the book; the corresponding items are marked with the asterisk.There are a number of courses dealing with special divisions of mathematical analysis, such as equations of mathematical physics, functions of a complex argument and the like, and the­ refore, although these divisions are important for mathematical education of an engineer, they are not treated in this book. We also draw attention to the fact that only a few questions related to approximate calculations and programming (e.g. the applica­ tion of the differential to approximate calculations, methods of approximate solution of equations, numerical integration and solutionof differential equations, etc.) are discussed inthiscourse. For a thorough study of this subject some other textbooks should be used.In this course many examples are given which demonstrate the application of mathematical analysis to various divisions of mechanics and physics. The study of these examples is very impor­ tant since the main interest of an engineer lies in solving concrete applied problems. At the end of each chapter we give a number of questions aimed at checking the understanding of the theore­ tical material. In the presentation of the material the main emphasis has been laid upon practical aspects, and some purely mathematical facts are given witnout proof. On the other hand, in some cases detailed proofs of theorems are given, especially when this elucidates the meaning of the theorem and shows in which way it can be applied. Besides, the study of the proofshelps the student to acquire practice in logical argument and provides prerequisites for further mathematical self-education.