The idea of designing this three-part problem book belongs to Professor B. Demidovich, but his early death prevented him from putting it into practice. The book was prepared by a group of us some of whom have had long pedagogical experience lecturing higher mathematics to engineering students. We have tried to do our best to develop and realize the ideas and plans of the late Professor Demidovich.The problems contained in the book cover all the branches of higher mathematics studied by engineering students. In addition, our problem book includes a number of problems which will enable the reader to repeat the main topics of mathe­ matical analysis and vector algebra from his school course, studying them more carefully.The present book (Part 1) entitled “Linear Algebra and Fundamentals of Mathematical Analysis” consists of seven chapters (1 to 7) and includes the topics which, as a rule, are studied during the first two semesters of the course. Among them are: vector algebra with elements of analytical geometry, linear algebra, and also differential calculus of functions of one and several variables, and integral cal­culus of functions of one variable.Each chapter is supplied with answers to all the compu­tational problems. The answers are given at the end of each chapter. Those problems marked with an * are provided with hints and the ones with **, with solutions to be found with answers.Each section in all chapters is supplied with a brief in­ troduction containing both the relevant theoretical material (definitions, formulas, and theorems) and a plenty of thor­ oughly worked examples.Contributing Authors:V.A. Bolgov, B.P. Demidovich, V.A. Efimenko,A.V. Efimov, A.F. Karakulin, S.M. Kogan, G.L. Lunts, E.F. Porshneva, A.S. Pospelov, S.V. Frolov, R.Ya. Shostak, A.R. YanpolskiiTranslated from the Russian by Leonid Levant