Vector Analysis, with Applications to Geometry and Physics

This book has been written primarily to facilitate the grasp of both the fundamental concepts and the techniques of vector analysis by the beginning student. In addition to its use as a beginning text on vector analysis, it should serve as a reference for advanced students, especially in the engineering and physical science fields. It is hoped that the numerous examples and exercises will make the book valuable to a large number of engineers for self-study. To carry out these objectives, the authors have included examples and exercises that illustrate many applications of the theory to geometry and physics. In addition to problems of standard types, many problems have been included which bring out more difficult aspects of the subject. They serve the dual purpose of introducing the student to a deeper appreciation of the subject and of indicating many applications which might not be apparent on a first reading. The first part of the book is devoted to the algebra and calculus of vectors and vector functions, and some of the simpler applications to geometry and physics are treated. Later chapters are concerned with specialized topics and more advanced types of applications. Chapters 8 to 11 discuss rather thoroughly the subjects of differential geometry, harmonic functions, and electricity and magnetism. The final chapter on linear vector functions introduces dyadic and their applications to geometry and physics.