Definition:Vector Analysis/Historical Note

Historical Note on Vector Analysis
One of the earliest attempts to develop a calculus for working directly on vectors was made by in $1679$, but this was unsuccessful.

's demonstration in $1806$ of a geometrical representation of the complex plane gave the misleading impression that vectors in the Cartesian plane required them to be represented as complex numbers, which held development back for some time.

published his in $1827$, which was the forerunner of the more general analysis of geometric forms developed by.

published in $1832$, which was one of the first works to deal systematically with addition and equality of vectors.

In $1843$, published  (that is: "Linear Extension Theory, a new branch of mathematics").

In $1844$, started publication of a series of articles in  discussing quaternions.

Both of these works developed the theory of vector analysis, independently of each other, from different directions.

Further development was due to, whose of $1867$ progressed the theory considerably.

However, the theory of quaternions was too complicated and theoretical to be much practical use in studying real-world problems.

As a result, several mathematical physicists worked on improving the system and developing more elementary techniques.

Important to this process were, , , , , and.

The approach of and  was not well received by, who was displeased with the fact that they did not use his beloved quaternions.

Contrariwise, and  did not appreciate the inflexibility of 's approach, being likened by them to (and ridiculed as) a religious ritual.

However, the approach of and  prevailed, and by the time of, their techniques had bedded in.

gleefully relates the controversy, standing four-square upon the side of and, as well he might; his presentation is thoroughly within their tradition.

and continued the work in developing vector algebra.

It is worth noting that many of the techniques of vector analysis were developed in response to the need to analyse Maxwell's equations in the field of electromagnetism.

Its application to mechanics happened later.