What is real analysis?
In this article, we answer the question: what is real analysis about? Apparently the word real comes from the set ...
Continuous functions of one variable
We discuss the important class of continuous functions of one variable. We teach you how to prove that a function ...
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 ...
Riemann Integral Exercises
Riemann integral exercises with detailed answers are offered on this page. These kinds of integrals of bounded function in bounded ...
Translation operator
We discuss the properties of the translation operator defined in a Lebesgue space. The latter appears in the study of ...
Primitives of continuous functions
Primitives of continuous functions play a key role in the calculation of integrals. Therefore, in this article, we will use ...
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 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 ...