Note on notation

As I observed once earlier, it is tricky to write mathematical text in a blog; there is no good way to write mathematical symbols (I do not think the blog software allows it; if any reader knows a way out of this, please let me know!). So I have to innovate. 

Here are the symbols I will use in this and future entries. (Some of you may recognize that I am merely following the input protocol of a computer algebra software which I use a great deal: Derive. I find it a very simple and logical notation.)

1. To denote the derivative of a function f(x) with respect to x, I write dif(f(x), x). For example, dif(x^2, x) = 2x.
2. The symbol dif(f(x), x, 2) denotes the second derivative of f(x) with respect to x; dif(f(x), x, 3) denotes the third derivative, and so on. For example, dif(x^3, x, 2) = 6x.
3. To denote the indefinite integral of f(x) with respect to x, I write int(f(x), x). For example, int(x^2, x) = x^3/3.
4. To denote the definite integral of f(x) with respect to x, evaluated between two given limits a and b, I write int(f(x), x, a, b). For example, int(x^2, x, 0, 1) = 1/3.
5. To denote the limit of f(x) as x tends to a, I write lim(f(x), x, a). For example, lim((x^2-a^2)/(x-a), x, a) = 2a.
6. If I want to specify the direction of approach, I use an additional symbol: lim(f(x), x, a, -1) indicates that x approaches a from the left, and lim(f(x), x, a, 1) indicates that x approaches a from the right.

More such notation will follow in due course. I think the systematic use of such notation will allow us to communicate more easily with each other.