Calculus 1, the mathematical wizardry behind change and motion, holds immense power in unraveling the secrets of our world. Whether you’re a high school student embarking on a mathematical adventure or a university student delving deeper into its mysteries, this article will be your

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

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

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

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

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

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

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

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

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

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

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