Vector analysis, which had its beginnings in the middle of the 19th century, has in recent years become an essential part of the mathematical background required of engineers, physicists, mathematicians and other scientists. This requirement is far from accidental, for not only does vector analysis provide a concise notation for presenting equations arising from mathematical formulations of physical and geometrical problems but it is also a natural aid in forming mental pictures of physical and geometrical ideas. In short, it might very well be considered a most rewarding language and mode of thought for the physical sciences. This book is designed to be used either as a textbook for a formal course in vector analysis or as a very useful supplement to all current standard texts. It should also be of considerable value to those taking courses in physics, mechanics, electromagnetic theory, aerodynamics or any of the numerous other fields in which vector methods are employed. Each chapter begins with a clear statement of pertinent definitions, principles and theorems together with illustrative and other descriptive material. This is followed by graded sets of solved and supplementary problems. The solved problems serve to illustrate and amplify the theory, bring into sharp focus those fine points without which the student continually feels himself on unsafe ground, and provide the repetition of basic principles so vital to effective teaching. Numerous proofs of theorems and derivations of formulas are included among the solved problems. The large number of supplementary problems with answers serve as a complete review of the material of each chapter. Topics covered include the algebra and the differential and integral calculus of vectors, Stokes' theorem, the divergence theorem and other integral theorems together with many applications drawn from various fields. Added features are the chapters on curvilinear coordinates and tensor analysis which should prove extremely useful in the study of advanced engineering, physics and mathematics. Considerably more material has been included here than can be covered in most first courses. This has been done to make the book more flexible, to provide a more useful book of reference, and to stimulate further interest in the topics. The author gratefully acknowledges his indebtedness to Mr. Henry Hayden for typographical layout and art work for the figures. The realism of these figures adds greatly to the effectiveness of presentation in a subject where spatial visualizations play such an important role. - McGraw Hill Education