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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 is a very important part of mathematics. In fact, the treatment of partial differential equations ...

In this article, we learn how to solve the heat equation using the Fourier series. The heat equation belongs to ...

In this article, we state and prove Gronwall lemma and give some of its applications. In fact, we will use ...

The stability analysis of solutions of differential equations is one of the most important axes in ODE. Here w gives ...

We propose a nice proof of Peano existence theorem. This theorem shows that the continuity of the vector field suffices ...

Welcome to the fascinating world of mathematics, where even and odd numbers reign supreme! These two categories of numbers are ...

In this post, we study Fourier transform properties and give some applications. In fact, this transformation helps in converting partial ...

In this post, we propose some tips on how to teach math to children. It pays to teach kids math ...

We will explore the matrix trace, its properties, and its significance in understanding the behavior of matrices. Although, matrices are ...

We offer a selection of improper integral exercises with detailed answers. Our main objective is to show you how to ...

We propose exercises on functions defined by integrals. We mainly prove the regularity of such a function, like continuity and ...