This volume is based on a series of lectures on matrix calculus and tensor calculus, and their applications, given under the sponsorship of the Engineering, Science, and Management War Training (ESMWT) program, from August 1942 to March 1943. The group taking the course included a considerable number of outstanding research engineers and directors of engineering research and development. I am very grateful to these men who welcomed me and by their interest in my lectures encouraged me.
The purpose of this book is to give the reader a working knowledge of the fundamentals of matrix calculus and tensor calculus, which he may apply to his own field. Mathematicians, physicists, meteorologists, and electrical en~eers, as well as mechaiucal and aeronautical e~gineers, will discover principles applicable to their respective fields. The last group, for instance, will find material on vibrations, aircraft flutter, elasticity, hydrodynamics, and fluid mechanics.