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