what-is-real-analysis

What is real analysis?

In this article, we answer the question: what is real analysis about? Apparently the word real comes from the set...
the-optimal-method-of-the-step-gradient

The optimal step gradient method

In this article, we propose an exercise that describes the optimal method of the step gradient for coercive functions on...
translation-operator

Translation operator

We discuss the properties of the translation operator defined in a Lebesgue space. The latter appears in the study of...
lyapunov-stability-for-nonlinear-systems

Lyapunov stability for nonlinear systems

We discuss the Lyapunov stability for nonlinear systems. Indeed, having a reference solution, a stationary solution, one wonders if the...
instability-of-solutions-to-nonlinear-systems

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...
open-mapping-theorem

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

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

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

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

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...
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