• Title: Partial d

• YouTube-Title: Advent of Mathematical Symbols - Part 28 - Partial d

• Bright video: https://youtu.be/uYlBnY4F__w

• Dark video: https://youtu.be/nuqMsGmkxuo

• Timestamps
• Subtitle in English

1 00:00:00,357 –> 00:00:03,450 Hello and welcome back to the next mathematical symbol.

2 00:00:03,500 –> 00:00:05,897 Which is today this partial d.

3 00:00:06,471 –> 00:00:11,715 I just call it partial d, but there are a lot of other names for this cursive d.

4 00:00:12,143 –> 00:00:16,275 However it’s important to see that it’s not a lower case delta.

5 00:00:16,814 –> 00:00:22,300 Of course it’s related, because it should look like a rounded version of a lower case d.

6 00:00:22,600 –> 00:00:28,578 Indeed some people just call this symbol del, but this can be confused with the nabla operator.

7 00:00:29,343 –> 00:00:33,597 Therefore if you pronounce this letter here, you can simply say d

8 00:00:33,797 –> 00:00:39,037 and now you might already know, we mostly use this symbol when we talk about partial derivatives.

9 00:00:39,414 –> 00:00:46,946 So for example, if we have a function from R^2 to R, we can form the derivative with respect to the first variable here

10 00:00:47,343 –> 00:00:51,416 and this is then the partial derivative, denoted with the curved d.

11 00:00:51,616 –> 00:00:54,918 So we have df over dx_1

12 00:00:55,329 –> 00:01:00,939 and then we simply say: this is the partial derivative of f with respect to x_1

13 00:01:01,771 –> 00:01:08,770 and there you see, we use this curved d to distinguish the partial derivative from a normal derivative in 1 variable.

14 00:01:09,286 –> 00:01:13,746 However, our partial d here is also used in other contexts.

15 00:01:14,386 –> 00:01:18,816 So for example in topology we talk about open and closed sets

16 00:01:19,016 –> 00:01:26,306 and then it turns out that for each subset in a given space, we can define the so called boundary of the set.

17 00:01:26,886 –> 00:01:31,272 In this picture here, we would visualize it as the shell of the given set A

18 00:01:31,657 –> 00:01:35,392 and then we denote this boundary by partial dA.

19 00:01:35,886 –> 00:01:42,259 So you see this is a completely different usage of this curved d, then we have it for the partial derivatives.

20 00:01:42,929 –> 00:01:48,091 Now, if you know other cases where the partial d is used, you can tell me in the comments.

21 00:01:48,529 –> 00:01:53,113 Otherwise I would say let’s meet in the next video about mathematical symbols.

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