Monte Carlo methods are computational algorithms that rely on random samples to obtain numerical results. In this article, we will see how to obtain the value of pi with these methods.
The number π is a mathematical constant: the ratio of a circle’s circumference to its diameter. In this article we walk through the history of π and learn a bit of Python programming along the way.
A good part of the study of calculus is devoted to what are called infinite series. But what, exactly, are infinite series? And how are they related to the paradox of Achilles and the tortoise, one of the so-called paradoxes of Zeno of Elea, the Greek philosopher? What is the connection with quantum mechanics and the uncertainty principle? And where does Python come in? That is what we will find out in this article.
We have already written here on the site about the concepts of limit and derivative and how we can do the related computations with Python. Continuing our journey through calculus, in this article we will see how to work with integrals using SymPy and SciPy, Python packages. Along the way, we will pick up some notions of numerical methods.
Engineers and scientists are always trying to get the most performance out of their equipment and projects at the lowest cost. This search gives rise to so-called optimization problems. In this article, we will see how to use Python, with the help of the SymPy package, to solve them.
The start of a calculus course tends to feel abstract because of the concept of a limit. But it soon becomes more tangible with the introduction of the derivative, which has many obvious practical applications. In this article, we will see how to work with derivatives using SymPy, a Python package.
The concept of a limit is the most important one in the study of calculus. Many other concepts and ideas are built on the definition of a limit. In this article, we will see how to find the limit of functions using SymPy and how this package can be a teaching aid in the study of calculus.
Complex numbers are fascinating and have many practical applications. In this article, we will see how Python handles complex numbers natively and how the SymPy package extends the power of the language.
What do ocean waves, soap bubbles, and DNA have in common? That is what I show in this article, with the help of Python. We will see how these subjects relate to trigonometric functions.
In this article we will see how to make plots with SymPy and Matplotlib. When people talk about SymPy, we usually focus on solving mathematical problems. But many forget that the library has some basic features for building plots, which we will see in this article.
A large part of fundamental math education is devoted to solving equations and systems of equations. In this article we will see how to use SymPy for these tasks quickly and intuitively.
