-
Notifications
You must be signed in to change notification settings - Fork 2
/
10_Mathematical_Notations_and_Special_Characters_eng.srt
1377 lines (1087 loc) · 21.5 KB
/
10_Mathematical_Notations_and_Special_Characters_eng.srt
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1
00:00:01,500 --> 00:00:03,600
This section of Introduction
to Wolfram Notebooks
2
00:00:03,600 --> 00:00:05,800
is about notations
like special characters
3
00:00:05,800 --> 00:00:08,000
and notations
used in mathematics.
4
00:00:08,000 --> 00:00:09,500
Much of this topic
can be illustrated
5
00:00:09,500 --> 00:00:11,000
by considering various ways
6
00:00:11,000 --> 00:00:12,900
of entering
this mathematical expression,
7
00:00:12,900 --> 00:00:15,000
which is a definite integral.
8
00:00:15,000 --> 00:00:17,700
One way of entering
this expression is with palettes.
9
00:00:17,700 --> 00:00:20,100
Start by opening
the Basic Math Assistant palette
10
00:00:20,100 --> 00:00:23,900
by choosing Basic Math Assistant
under the Palettes menu.
11
00:00:23,900 --> 00:00:26,300
Each section of this palette
shows a grid of buttons
12
00:00:26,300 --> 00:00:28,300
for pasting things
into the notebook.
13
00:00:28,300 --> 00:00:29,300
There are keyboard commands
14
00:00:29,300 --> 00:00:31,000
for entering all
of these things as well,
15
00:00:31,000 --> 00:00:32,600
which will be described
in a moment,
16
00:00:32,600 --> 00:00:34,800
but we will start
with the palette.
17
00:00:34,800 --> 00:00:36,700
All of the buttons
that are needed for this input
18
00:00:36,700 --> 00:00:39,000
are in the section
labeled Typesetting.
19
00:00:39,000 --> 00:00:40,650
Within this section,
under the first tab
20
00:00:40,650 --> 00:00:42,600
are buttons for
mathematical notations
21
00:00:42,600 --> 00:00:44,600
like fractions and exponents,
22
00:00:44,600 --> 00:00:46,800
and under the second tab
are buttons for entering
23
00:00:46,800 --> 00:00:49,200
special symbols
and Greek letters.
24
00:00:49,200 --> 00:00:50,900
Returning to the first tab,
we can start
25
00:00:50,900 --> 00:00:53,500
by clicking the button
that shows the definite integral,
26
00:00:53,500 --> 00:00:56,300
which enters into the notebook
a template with empty boxes,
27
00:00:56,300 --> 00:00:59,100
called placeholders, for entering
parts of the integral.
28
00:00:59,100 --> 00:01:00,900
The lower limit of integration
29
00:01:00,900 --> 00:01:02,650
is highlighted
with a colored background,
30
00:01:02,650 --> 00:01:04,950
to indicate
where input will appear.
31
00:01:04,950 --> 00:01:07,600
In this example, the lower limit
of integration is 0,
32
00:01:07,600 --> 00:01:09,000
so enter 0,
33
00:01:09,000 --> 00:01:11,900
then press the TAB key
to move to the next placeholder,
34
00:01:11,900 --> 00:01:14,200
which is the upper limit
of integration.
35
00:01:14,200 --> 00:01:16,000
The upper limit of integration
in this example
36
00:01:16,000 --> 00:01:17,300
is a special character,
37
00:01:17,300 --> 00:01:20,000
which is the mathematical symbol
for infinity.
38
00:01:20,000 --> 00:01:22,100
To enter that symbol,
click the second tab
39
00:01:22,100 --> 00:01:25,600
to open the grid of buttons
for symbols and Greek letters,
40
00:01:25,600 --> 00:01:27,600
and enter the upper limit
of integration,
41
00:01:27,600 --> 00:01:30,300
by clicking the infinity button
in the palette.
42
00:01:30,300 --> 00:01:32,750
Then press the TAB key
to move to the next placeholder
43
00:01:32,750 --> 00:01:35,000
in the template,
which is the integrand.
44
00:01:35,000 --> 00:01:37,200
The first part of the integrand
is an exponential,
45
00:01:37,200 --> 00:01:39,100
which is under the first tab.
46
00:01:39,100 --> 00:01:41,400
Pressing the button
for an exponential
47
00:01:41,400 --> 00:01:42,900
enters that template.
48
00:01:42,900 --> 00:01:46,000
Then return to the second tab
to enter the exponential <i>e</i>
49
00:01:46,000 --> 00:01:48,900
and press the TAB key
to move to the next placeholder,
50
00:01:48,900 --> 00:01:50,500
which is the exponent.
51
00:01:50,500 --> 00:01:53,900
Now enter the exponent,
which is –2<i>x</i>.
52
00:01:53,900 --> 00:01:55,300
Continuing to type at this point
53
00:01:55,300 --> 00:01:57,200
would enter more input
into the exponent,
54
00:01:57,200 --> 00:01:59,000
but to continue
with this example,
55
00:01:59,000 --> 00:02:01,400
it is necessary to get out
of the exponent.
56
00:02:01,400 --> 00:02:03,400
The keyboard command
to end the exponent
57
00:02:03,400 --> 00:02:05,000
and move to
the enclosing expression
58
00:02:05,000 --> 00:02:06,600
is CONTROL+SPACE.
59
00:02:06,600 --> 00:02:08,900
So with the insertion point
in the exponent,
60
00:02:08,900 --> 00:02:10,000
press CONTROL+SPACE
61
00:02:10,000 --> 00:02:12,800
and then finish
entering the integrand.
62
00:02:12,800 --> 00:02:14,200
You could also move
the insertion point
63
00:02:14,200 --> 00:02:16,500
out of the exponent
by clicking the mouse
64
00:02:16,500 --> 00:02:18,500
outside of the exponent.
65
00:02:18,500 --> 00:02:20,950
Now press the TAB key
to move to the next placeholder
66
00:02:20,950 --> 00:02:23,000
and enter <i>x</i>
to complete the input.
67
00:02:23,000 --> 00:02:24,000
This is a live input
68
00:02:24,000 --> 00:02:26,200
and can be evaluated
just like any other input
69
00:02:26,200 --> 00:02:29,500
to do that calculation
and get a result.
70
00:02:29,500 --> 00:02:32,500
The input is still not formatted
quite like the initial example.
71
00:02:32,500 --> 00:02:34,400
There are several differences
in alignment
72
00:02:34,400 --> 00:02:36,500
and in the shapes of characters.
73
00:02:36,500 --> 00:02:39,400
Those differences are there
because the example is shown
74
00:02:39,400 --> 00:02:41,500
in a format
called TraditionalForm
75
00:02:41,500 --> 00:02:43,000
and the input
that we just entered
76
00:02:43,000 --> 00:02:45,000
is shown in StandardForm.
77
00:02:45,000 --> 00:02:47,300
StandardForm can be converted
to TraditionalForm
78
00:02:47,300 --> 00:02:49,000
by selecting the input
and choosing
79
00:02:49,000 --> 00:02:52,000
Convert To ► TraditionalForm
under the Cell menu.
80
00:02:52,000 --> 00:02:54,500
TraditionalForm looks more like
traditional mathematics,
81
00:02:54,500 --> 00:02:56,350
which is frequently desirable,
82
00:02:56,350 --> 00:02:57,350
and the only reason
83
00:02:57,350 --> 00:02:58,900
that TraditionalForm
isn't the default
84
00:02:58,900 --> 00:03:02,000
is that translating traditional
mathematics into computer input
85
00:03:02,000 --> 00:03:03,300
requires a somewhat
86
00:03:03,300 --> 00:03:06,500
elaborate and nonuniform set
of translation rules.
87
00:03:06,500 --> 00:03:09,000
For example, in StandardForm
functions are shown
88
00:03:09,000 --> 00:03:11,000
with square brackets
around the arguments,
89
00:03:11,000 --> 00:03:12,200
but in TraditionalForm
90
00:03:12,200 --> 00:03:15,000
function arguments
are enclosed in parentheses.
91
00:03:15,000 --> 00:03:18,200
This use of parentheses
is a potential ambiguity, however,
92
00:03:18,200 --> 00:03:20,400
because parentheses
can also indicate
93
00:03:20,400 --> 00:03:21,700
arithmetic grouping
94
00:03:21,700 --> 00:03:24,000
and the computer
cannot always guess correctly
95
00:03:24,000 --> 00:03:27,400
what the parentheses should mean
in every situation.
96
00:03:27,400 --> 00:03:28,500
As a practical matter though,
97
00:03:28,500 --> 00:03:30,650
the rules for translating
TraditionalForm input
98
00:03:30,650 --> 00:03:31,650
work pretty well.
99
00:03:31,650 --> 00:03:33,500
So if you prefer TraditionalForm,
100
00:03:33,500 --> 00:03:36,000
it is entirely reasonable
to use it,
101
00:03:36,000 --> 00:03:38,900
and if it is only being used
for display and not for input,
102
00:03:38,900 --> 00:03:42,000
than there is no real problem
with it at all.
103
00:03:42,000 --> 00:03:43,800
This input
and all of these notations
104
00:03:43,800 --> 00:03:45,900
can also be entered
using keyboard commands.
105
00:03:45,900 --> 00:03:47,650
One way to learn
about keyboard commands
106
00:03:47,650 --> 00:03:48,950
is by hovering the mouse
107
00:03:48,950 --> 00:03:51,500
over a corresponding button
in the palette.
108
00:03:51,500 --> 00:03:53,000
For example,
hovering the mouse pointer
109
00:03:53,000 --> 00:03:55,500
over the exponential <i>e</i> button
in this palette
110
00:03:55,500 --> 00:03:57,800
gives a display called a tooltip
111
00:03:57,800 --> 00:03:59,600
that shows the name
of the character,
112
00:03:59,600 --> 00:04:01,200
which is exponential <i>e</i>,
113
00:04:01,200 --> 00:04:05,100
and the keyboard command,
which is ESCAPE+ee+ESCAPE.
114
00:04:05,100 --> 00:04:06,650
Typing ESCAPE+ee+ESCAPE
115
00:04:06,650 --> 00:04:09,000
on the keyboard enters
the exponential constant <i>e</i>
116
00:04:09,000 --> 00:04:11,100
that came up in the example.
117
00:04:11,100 --> 00:04:13,500
There are also keyboard commands
for mathematical templates.
118
00:04:13,500 --> 00:04:16,500
For example, under the tab
for typesetting forms,
119
00:04:16,500 --> 00:04:18,000
hovering the mouse
over the button
120
00:04:18,000 --> 00:04:19,900
for entering
a definite integral
121
00:04:19,900 --> 00:04:24,000
shows the command
ESCAPE+dintt+ESCAPE,
122
00:04:24,000 --> 00:04:25,500
which can be typed
from the keyboard
123
00:04:25,500 --> 00:04:28,000
to get the definite
integral template.
124
00:04:28,000 --> 00:04:29,450
The names of keyboard commands
125
00:04:29,450 --> 00:04:32,000
are chosen to have some
logical way of remembering them.
126
00:04:32,000 --> 00:04:35,000
For example, the keyboard command
for the integral character
127
00:04:35,000 --> 00:04:37,000
is ESCAPE+int+ESCAPE
128
00:04:37,000 --> 00:04:39,850
and the keyboard command
for the definite integral template
129
00:04:39,850 --> 00:04:42,200
is ESCAPE+dintt+ESCAPE,
130
00:04:42,200 --> 00:04:46,500
where "d-i-n-t-t" is short
for definite integral template.
131
00:04:46,500 --> 00:04:47,800
To continue with the input,
132
00:04:47,800 --> 00:04:49,300
enter the lower limit
of integration,
133
00:04:49,300 --> 00:04:50,400
then press the TAB key
134
00:04:50,400 --> 00:04:52,500
to move to the upper limit
of integration.
135
00:04:52,500 --> 00:04:54,700
The keyboard command
for the infinity character
136
00:04:54,700 --> 00:04:56,900
is ESCAPE+inf+ESCAPE.
137
00:04:56,900 --> 00:04:59,800
Then press the TAB key
to move to the integrand.
138
00:04:59,800 --> 00:05:02,500
ESCAPE+ee+ESCAPE
enters the exponential <i>e</i>
139
00:05:02,500 --> 00:05:05,800
and CONTROL+6
gives a template for the exponent.
140
00:05:05,800 --> 00:05:08,400
On common keyboards
the caret character,
141
00:05:08,400 --> 00:05:10,400
which is used in computer code
for exponents,
142
00:05:10,400 --> 00:05:12,400
is on the key for the number 6,
143
00:05:12,400 --> 00:05:15,000
so a good way to remember
CONTROL+6 for an exponent
144
00:05:15,000 --> 00:05:17,100
is that it is the CONTROL key
145
00:05:17,100 --> 00:05:19,500
and the key
with the caret character on it.
146
00:05:19,500 --> 00:05:21,900
Then enter the exponent
and press the TAB key
147
00:05:21,900 --> 00:05:25,500
to move to the last placeholder
and complete the input.
148
00:05:25,500 --> 00:05:27,900
This input could have been
entered in many different ways.
149
00:05:27,900 --> 00:05:29,800
For example,
to enter the exponential
150
00:05:29,800 --> 00:05:31,400
rather than starting
with the template,
151
00:05:31,400 --> 00:05:33,500
we can start with
the exponential <i>e</i> character,
152
00:05:33,500 --> 00:05:34,900
select that character
153
00:05:34,900 --> 00:05:37,200
and then click the button
for the template.
154
00:05:37,200 --> 00:05:40,100
This had the effect of inserting
the exponential <i>e</i> character
155
00:05:40,100 --> 00:05:41,800
in place of the filled
black square
156
00:05:41,800 --> 00:05:43,500
that is shown on the button.
157
00:05:43,500 --> 00:05:44,800
Several of the buttons
in this palette
158
00:05:44,800 --> 00:05:47,000
have placeholders
that are filled black squares
159
00:05:47,000 --> 00:05:49,000
rather than empty black squares.
160
00:05:49,000 --> 00:05:51,800
The filled black squares
are selection placeholders,
161
00:05:51,800 --> 00:05:54,300
which work just like
the empty square placeholders
162
00:05:54,300 --> 00:05:56,900
except that if something
in the notebook is selected
163
00:05:56,900 --> 00:05:57,700
when one of those buttons
164
00:05:57,700 --> 00:06:01,300
with a filled black square
selection placeholder is clicked,
165
00:06:01,300 --> 00:06:03,200
then the selected expression
gets inserted
166
00:06:03,200 --> 00:06:05,500
in place of
the selection placeholder.
167
00:06:05,500 --> 00:06:07,650
For example,
the definite integral example
168
00:06:07,650 --> 00:06:08,650
could have been entered
169
00:06:08,650 --> 00:06:11,500
by starting
with the inner expression.
170
00:06:11,500 --> 00:06:13,900
The button that was used
earlier for entering
171
00:06:13,900 --> 00:06:15,800
the definite integral template
does not have
172
00:06:15,800 --> 00:06:17,800
a filled black square
selection placeholder,
173
00:06:17,800 --> 00:06:19,050
but there is a similar button
174
00:06:19,050 --> 00:06:21,200
in the Basic Commands section
of the palette
175
00:06:21,200 --> 00:06:23,500
that does have
a selection placeholder.
176
00:06:23,500 --> 00:06:25,750
To enter the input,
select the expression
177
00:06:25,750 --> 00:06:27,100
and click the button,
178
00:06:27,100 --> 00:06:28,650
which inserts
the selected expression
179
00:06:28,650 --> 00:06:31,400
in place
of the selection placeholder.
180
00:06:31,400 --> 00:06:32,600
This template is also different
181
00:06:32,600 --> 00:06:34,500
in that it has
descriptive placeholders
182
00:06:34,500 --> 00:06:36,500
that display as shaded boxes
183
00:06:36,500 --> 00:06:40,100
with reminders about the purpose
of each part of the input.
184
00:06:40,100 --> 00:06:41,300
These descriptive placeholders
185
00:06:41,300 --> 00:06:43,300
work just like
the empty box placeholders
186
00:06:43,300 --> 00:06:47,400
and can be filled in just as
before to complete the input.
187
00:06:47,400 --> 00:06:49,200
All of these notations
and special characters
188
00:06:49,200 --> 00:06:51,800
can be used in Text cells
and in graphics
189
00:06:51,800 --> 00:06:54,000
and almost anywhere else
in the notebook.
190
00:06:54,000 --> 00:06:56,000
For example, here is a Text cell
191
00:06:56,000 --> 00:06:59,200
with some mathematical notations
within the text.
192
00:06:59,200 --> 00:07:00,800
This Text cell can be entered
193
00:07:00,800 --> 00:07:04,000
using much the same process
as was used for entering input.
194
00:07:04,000 --> 00:07:06,500
Start with a Text cell
and use either the palette
195
00:07:06,500 --> 00:07:10,800
or keyboard commands
to enter mathematical notations.
196
00:07:10,800 --> 00:07:12,800
An important aspect
of this Text cell
197
00:07:12,800 --> 00:07:14,500
is that the formatted mathematics
198
00:07:14,500 --> 00:07:17,800
is actually in a separate cell
called an Inline cell.
199
00:07:17,800 --> 00:07:19,500
Clicking within
the formatted mathematics
200
00:07:19,500 --> 00:07:22,500
changes the background color
to highlight the Inline cell.
201
00:07:22,500 --> 00:07:25,000
To leave the Inline cell
and continue entering text,
202
00:07:25,000 --> 00:07:27,600
you can either
click beyond the Inline cell
203
00:07:27,600 --> 00:07:29,400
or press CONTROL+0,
204
00:07:29,400 --> 00:07:33,000
which is the keyboard command
to end the Inline cell.
205
00:07:33,000 --> 00:07:35,700
In that example, the Inline cell
was created automatically
206
00:07:35,700 --> 00:07:38,500
as soon as some notation
other than text was entered,
207
00:07:38,500 --> 00:07:39,750
but in general it is necessary
208
00:07:39,750 --> 00:07:41,600
to first create
a new Inline cell,
209
00:07:41,600 --> 00:07:44,000
which you can do
by choosing Start Inline Cell
210
00:07:44,000 --> 00:07:46,700
from the Typesetting menu
under the Insert menu,
211
00:07:46,700 --> 00:07:49,400
and right below that