Instability of solutions to nonlinear systems
In this post, we propose two results in the instability of solutions to nonlinear systems. Here, we study ordinary differential ...
Direct sum of subspaces examples
The philosophy behind the direct sum of subspaces is the decomposition of vector spaces as a sum of disjoint spaces. ...
Open mapping theorem in functional analysis
In this article, we give an application of the open mapping theorem in functional analysis. This fundamental theorem in functional ...
Differential calculus in Banach spaces
Differential calculus in Banach spaces is a very important part of mathematics. In fact, the treatment of partial differential equations ...
Heat equation using the Fourier series
In this article, we learn how to solve the heat equation using the Fourier series. The heat equation belongs to ...
Gronwall lemma
In this article, we state and prove Gronwall lemma and give some of its applications. In fact, we will use ...
Stability analysis of differential equations
The stability analysis of solutions of differential equations is one of the most important axes in ODE. Here w gives ...
Proof of peano existence theorem
We propose a nice proof of Peano existence theorem. This theorem shows that the continuity of the vector field suffices ...
Even and odd numbers
Welcome to the fascinating world of mathematics, where even and odd numbers reign supreme! These two categories of numbers are ...
Fourier Transform properties and applications
In this post, we study Fourier transform properties and give some applications. In fact, this transformation helps in converting partial ...
How to teach math to children: tips for parents
In this post, we propose some tips on how to teach math to children. It pays to teach kids math ...
Matrix trace worksheet
We will explore the matrix trace, its properties, and its significance in understanding the behavior of matrices. Although, matrices are ...