Knowledge base dedicated to Linux and applied mathematics.
We are going tho show that the kernel of a group homomorphism is a normal subgroup. Next, we prove that every normal subgroup is the kernel of a (...) Read More »
How to write matrices in Latex ? matrix, pmatrix, bmatrix, vmatrix, Vmatrix. Here are few examples to write quickly (...) Read More »
We prove here that the sine function sin (-x) = - sin x is odd using the unit circle. Read More »
We prove here that the cosine function cos(-x)=cos x is even using the unit circle. Read More »
In this section, we shall study the polynomial interpolation in the form of Newton. Given a sequence of (n+1) data points and a function f, the (...) Read More »
Derivative of composite function (g ∘ f) (g circle f), chain rule is defined by (g ∘ f)’(x) = g’(f(x)) × f’(x) . Derivative of composite function (u ∘ (...) Read More »
How to write Latex imaginary part symbol of a complex number? The real number b is called the imaginary part of the complex number a + (...) Read More »
How to write Latex real part symbol of a complex number? The real number a is called the real part of the complex number a + (...) Read More »
How to write Latex tensor product symbol ? Given two vectors v, w, we can form a tensor using the outer product, which is denoted v ⊗ (...) Read More »
Latex how to write backslash in Latex with or without amssymb : backslash , setminus, smallsetminus Read More »
How to write convolution symbol using Latex ? In function analysis, the convolution of f and g f∗g is defined as the integral of the product of (...) Read More »
Chebyshev polynomials are a useful and important tool in the field of interpolation. Indeed, in order to minimize the error in Lagrange (...) Read More »
How to use and define arrows symbols in latex. Latex Up and down arrows, Latex Left and right arrows, Latex Direction and Maps to arrow and Latex (...) Read More »
How to write jacobian symbol in Latex ? The jacobian matrix of vector-valued function f is the matrix of all its first-order partial (...) Read More »
How to write gradient symbol in Latex ? The gradient of a differentiable function f of several variables is the vector field whose components are (...) Read More »
Derivative of the inverse function f^-1 is given by : (f^-1)’(x)=1 / f’ (f^-1(x)) To prove this result, we are going to apply the Chain rule (...) Read More »
Derivative f’ of the function f(x)=exp x is: f’(x) = exp x for any value of x. Read More »
Derivative f’ of the function f(x)=sinx is: f’(x) = cos x for any value of x. Read More »
Derivative f’ of the function f(x)=tan x is: f’(x) = 1 + tan²x for any value x different of π/2 + kπ avec k ∈Z Read More »