Ever since the development of Quaternion analysis, by Sir William Rowan Hamilton, and of the "Ausdehnungslehre," by Grassmann, there has been a growing feeling that the older and more common processes of analysis were in some way artificial and complex. This fact exists, for it is such, because these newer methods and ideas apply more naturally, more simple and more directly to may of the conceptions of geometry, mechanics and mathematical physics, than those long accepted. One who has studied and labored over the applications of mathematical analysis to physical and geometrical problems, naturally has reluctance to discard the old familiar looking formulae and started anew in an unknown and radically different language.

This book is suitable for students and professionals in the fields of physics, engineering, and applied mathematics who seek a solid foundation in vector analysis. Its historical context also provides valuable insights into the evolution of mathematical methods in the early 20th century.