Mathematical Symbols are very important to learn mathematics, on using symbols we can easily understand the concepts of topics.
Generally, Mathematical Symbols can be categorized on their importance in the following ways:
- Mathematics symbols - Number
- Mathematics symbols - Basic
- Mathematics symbols - Algebraic
- Mathematics symbols - Geometric
- Mathematics symbols - Trigonometry
- Mathematics symbols - Set Theory
- Mathematics symbols - Statistics & Probability
- Mathematics symbols - Calculus And Analysis
- Mathematics symbols - Logical
- Mathematics symbols - Roman
- Mathematics symbols - Greek
- Mathematics symbols - Miscellaneous
Now we shall learn /discuss the eighth topic of Mathematical symbols - Calculus and Analysis on this post.
Mathematics symbols
These are very important Basic Tools frequently used by us not only in Calculus and Analysis but also in Physics, Chemistry, Economics as well as in other branches of applied mathematical sciences, humanities, and engineering.
Table of important Mathematical Symbol of Calculus and Analysis
Symbol
|
Name of Symbol
|
Definition / Meaning
|
Illustration
|
(a, b)
|
open interval
|
(a, b) = {x: a < x < b} or
(a, b) = {x / a < x < b}
|
Terminal / End points are not included (Excluded).
|
[a, b]
|
closed interval
|
[a, b] = {x: a ≤ x ≤ b} or
[a, b] = {x / a ≤ x ≤ b}
|
Terminal / End points are also included (Not Excluded).
|
|
Limit
|
Limit value of any function f
|
If value of function is not determined then calculated like, Evaluation
of f(2), when f(x) = 1/(x-2)
|
|
LHL
|
Left Hand Limit
|
|
|
RHL
|
Left Hand Limit
|
|
f(a) or g(x)
|
|
Value of function
|
Value of function f(x) or g(x) when
x = a.
|
|
Epsilon
|
It represents very
small number, near to zero.
|
|
e
|
Euler’s Number
|
It lies between 2 and 3,
e = 2.718281828…
|
|
dy/dx
|
Derivative
|
Derivative- Leibnitz’s Symbol
|
d(x4)/dx= 4x3
|
Dxy or D
|
Derivative
|
Derivative- Euler’s General
Notation/Symbol
|
D(x4) = 4x3
|
Dx2y or D
|
Derivative
|
Derivative of Derivative- Euler’s
Notation/Symbol
|
D2(x4) = 4.3x2=
12x2
|
Dx3y or D
|
Derivative
|
Three times Derivative - Euler’s
Notation/Symbol
|
D3(x4) = 4.3.2x=
24x
|
Dxny or D
|
Derivative
|
n times Derivative - Euler’s
Notation/Symbol
|
D’n(x4) = 0
|
Y’
|
Derivative
|
Derivative- Lagrange’s Symbol
|
(x4)’ = 4x3
|
Y’’
|
Second Derivative
|
Derivative of Derivative Lagrange’s
Symbol
|
(x4)’’ = 4.3x2=
12x2
|
Y’’’
|
Third Derivative
|
Three times Derivative- Lagrange’s
Symbol
|
(x4)’’’ = 4.3.2x= 24x
|
Y(n)
|
nth Derivative
|
n times Derivative- Lagrange’s
Symbol
|
(x4)’n = 0
|
∫
|
integral
|
Inverse process of differentiation
|
∫1. dx= x
|
∫∫
|
Double integral
|
Integration of two variable
functions
|
∫∫f (x, y) dxdy
Or
∫∫f (x, y)
dydx
|
∫∫∫
|
Triple integral
|
Integration of three variable
functions
|
∫∫∫f (x, y, z) dxdydz
|
∮
|
|
Closed contour integral / line
integral
|
∮f(x)dx
or
∮f(y)dy
|
∯
|
|
Closed surface integral
|
∯ f (x, y) dxdy
Or
∯ f (x, y) dydx
|
∰
|
|
Closed volume integral
|
∰ f (x, y, z) dxdydz
|
z
|
Complex number
|
A number having real or imaginary
parts
|
Z = a + i b, where a & b
both are Real Numbers
|
i
|
iota
|
Imaginary unit
|
i ≡ √-1
or
i2 = -1
or
i3 = -i
or
i4
= 1
|
R(z) or Re(z)
|
Real part of complex number
|
If z = a + i b then R(z) = a
|
If z = 3 +i4 then
R(z) = 3
|
I(z) or Im(z)
|
Imaginary part of complex number
|
If z = a +ib then I(z) = a
|
If z = 3 +i4 then
I(z) = 4
|
Z*
|
Complex conjugate
|
If z = a +ib then Z* = a - ib
|
If z = 3 +i4 then
Z* = 3-
i4
|
Z bar
|
Complex conjugate
|
If z = a +ib then Z(bar) = a
- ib
|
If z = 3 +i4 then
Z* = 3-
i4
|
|z|
|
Magnitude of a complex number
|
If z = a +ib then |Z|= √(a2+b2)
|
If z = 3 +i4 then
|3 +4i| = √25 = 5
|
|z|
|
Absolute value of a complex number
|
If z = a +ib then |Z|= √(a2+b2)
|
If z = 3 +i4 then
|3 +4i| = √25 = 5
|
Arg(z)
|
Argument value of a complex number
|
The angle made by the radius in the
Argand or complex plane.
|
If z= 1 + i then
arg(z)= pie /4
|