Mathematical Symbols - Calculus and Analysis

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:

1. Mathematics symbols - Number
2. Mathematics symbols - Basic
3. Mathematics symbols - Algebraic
4. Mathematics symbols - Geometric
5. Mathematics symbols - Trigonometry
6. Mathematics symbols - Set Theory
7. Mathematics symbols - Statistics & Probability
8. Mathematics symbols - Calculus And Analysis
9. Mathematics symbols - Logical
10. Mathematics symbols - Roman
11. Mathematics symbols - Greek
12. 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