## 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 is continuous.

## 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 spaces of

## Riemann Integral Exercises

Riemann integral exercises with detailed answers are offered on this page. These kinds of integrals of bounded function in bounded intervals, almost

## Translation operator

We discuss the properties of the translation operator defined in a Lebesgue space. The latter appears in the study of differential equations,

## Primitives of continuous functions

Primitives of continuous functions play a key role in the calculation of integrals. Therefore, in this article, we will use examples to

## 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 equations. Well-know

## 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 analysis plays

## 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 strongly depends

## 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 the class

## Gronwall lemma

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

## 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 a concise