The most important thing in Algebra - Euler

Quote from The Elements of Algebra - Leonard Euler Translated from French by John Hewlett, 1822:
"
It is of the utmost importance through the whole of Algebra, that a precise idea should be formed of those negative quantities. I shall, however, content myself with remarking here, that all such expressions as

+1 - 1, +2 - 2, +3 - 3, +4 - 4, &c.

are equal to 0, or nothing. And that

+2 - 5 is equal to - 3:

for if a person has 2 crowns, and owes 5, he has not only nothing, but still owes 3 crowns.
"
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If I spend as much money as I earn, then I'll have nothing at the end of the day of the paycheck. If I spend more than I earn, then I'll have not only nothing but also I have to do something extra to make it even that is still nothing.

Vector Analysis

The purpose of vector analysis is to acquire a thorough understanding of the mathematical methods required to deal with fields.

Mathematically, a field is a function that describes a physical quantity at all points in space. In scalar fields this physical quantity is completely specified by a single number for each point. For vector fields both a number and a direction are required.

A vector can be specified by its components:

scalar (or dot) product:

vector (or cross) product:



Wheatstone Bridge Circuit Analysis - continued 1

* Heaviside, "Bridge for Measuring a Given Resistance with a Given Galvanometer and Battery", Philosophical Magazine 1873.

Wheatstone Bridge Circuit Analysis: the current through the Galvanometer?

* Schwendler, "on the Galvanometer Resistance", Philosophical Magazine 1866

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p.s. I found some mistakes that I made when I was rewriting the equations from the original scrap paper to the above Inkpad. The mistakes were corrected as much as I could on 02-04-2011.