Calculus

We propose a nice proof of Peano existence theorem. This theorem shows that the continuity of the vector field suffices ...

In this post, we study Fourier transform properties and give some applications. In fact, this transformation helps in converting partial ...

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

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

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

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

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

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

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

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

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

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