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This book is designed to be used as a text book for formal courses in vector and sound waves or as a supplement to all current standard texts. It should also be of considerable value to those taking courses in physics, mechanics, aerodynamics, astrophysics and or any other numerous other fields in which vector and sound waves are employed.This book discuses the theory from its beginning. The foundation have been laid very carefully and the treatment is rigorous and on modern lines. It opens with a brief outlines of the essential properties of vector, waves and sound waves and their application in real life. Each chapter begins with a clear statement of pertinent definitions, principal and theory with mathematical description.