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 existence of...
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 to ODE....
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 an improper...
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 functions can...
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 a function...
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 of some...
