11 Analysis

chart
#= ∞ U+221e infinity
&s ∑ U+2211 summation sign
&p ∏ U+22of Product characters
* lower limit (rear lower Index)
/ upper limit (rear upper Index)
0 linked to (Kreis, Kuller)
$l log, lg logarithm
$8l ln logarithm naturalis
$4l ld logarithm dualis
$1l antilog antilogarithm
$3l cpllog supplementary or complementary logarithm
$e exp exponential function
$n num number
$( arg Argument
! ∫ U+222b integral
!! ∬ U+222c double integral
!0 ∮ U+222e contour integral
!!0 ∯ U+222f cover integral
!;3 ⨜ U+2a1c lower integral
!3 ⨛ U+2a1b upper integral
^! Integral special kind
@l integral stroke
9 Derivation stroke
2 derivation point
%d ∂ U+2202 (for partial derivative)
? ∂ U+2202 (for partial derivative) [Russia]
&d ∆ U+2206 big delta as a difference sign
#l lim Limes
#l;3 # l <: lim Limes inferior
#l3 # l: lim Limes superior

Russian Chart

!0- ∱ U+2231 clockwise contour integral
!06 ⨑ U+2a11 counter-clockwise contour integral

11.1 Functions


#= ∞ U+221e infinity
&s ∑ U+2211 summation sign
&p ∏ U+22of Product characters
* lower limit (lower index)
/ upper limit (upper index)
0 linked to (Kreis, Kuller)

The sum and product characters are lower and upper Borders according to the template as lower and upper indices played. According to the speech, in the Braille initially indicated the lower limit. Before that on the The following expression is usually included Spaces.

11.2 Logarithmic and Exponential Functions

chart
$l log, lg logarithm
$8l ln logarithm naturalis
$4l ld logarithm dualis
$1l antilog antilogarithm
$3l cpllog supplementary or complementary logarithm
$e exp exponential function
$n num number
$( arg Argument

The symbols listed above will be alike for everyone Variants of the relevant shorthand symbols in the black box used font. The symbols in braille are standing also for both upper and lower case Short word symbols.

Starts the argument with an indicator sign (for Example of numbers or uppercase or lowercase letters), it may connect to the symbol. In other cases, a blank sign between symbol and argument. It is generally permissible to use these symbols with the general Nouns for shorthand symbols ] and in to form the black letter usual letter. For example can also be written ]log for ]l (see "3.6 Short-term symbols"). These expressions are longer. but be useful there, where upper and lower case Short word symbols, a closer be maintained with the inkprint or the reader a familiarity with isolated occurring Symbols can not be assumed.

11.3 Integral and differential calculus

chart
! ∫ U+222b integral
!! ∬ U+222c double integral
!0 ∮ U+222e contour integral
!!0 ∯ U+222f cover integral
!;3 lower integral
!3 upper integral
^! Integral special kind
* lower limit (rear lower Index)
/ upper limit (rear upper Index)
@l integral stroke
9 Derivation stroke
2 derivation point
%d ∂ U+2202 round d (for partial derivative)
? ∂ U+2202 (for partial derivative) [Russia]
&d ∆ U+2206 big delta as a difference sign
#l lim Limes
#l;3 # l <: lim Limes inferior
#l3 # l: lim Limes superior

Lower and upper bounds are set according to the template as reproduced lower and upper indices. The way of speaking following you first enter the lower limit. Before the the following expression usually has a space.