## 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 for the

## 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 differential equations

## Improper integral exercises

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

## Functions defined by integrals

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

## How to find the limit of a function?

We propose simple techniques to learn you how to find the limit of a function. We first recall what a limit of

## Learning basic to advanced math

We offer practical tips for learning basic to advanced math. Above all, mathematics is a difficult and abstract subject, while a part

## Parameter dependent integral

Parameter-dependent integral is studied in this article. We propose a selection of exercises on continuity, limit, and differentiability of such parametric integrals.

## Exercises on convex functions and applications

In this article, we offer exercises on convex functions. In fact, our objectives are: to be able to show that a function

## Recurring sequences exercises

Recurring sequences are generally involved in the modeling of discrete systems. In fact, such sequences replace the differential equation by discretizing the

## Convergence of sequences

We discuss the convergence of sequences and how to calculate the limit of a sequence. This subject is fundamental in real analysis

## Exercises on differential calculus

We offer exercises on differential calculus with detailed answers. In fact, our objectives are as follows: knowing how to calculate the derivative

## Maximal solution to Cauchy problems

The maximal solution to Cauchy’s problems is a solution that gives full information on the physical model. In fact, we obtain this