The Fourier Series

Pure mathematics is much more than an armory of tools and techniques for the applied mathematician. On the other hand, the pure mathematician has ever been grateful to applied mathematics for stimulus and inspiration. From the vibrations of the violin string they have drawn enchanting harmonies of Fourier Series, and to study the triode valve they have invented a whole theory of non-linear oscillations.

George Frederick James Temple In 100 Years of Mathematics: a Personal Viewpoint (1981).


Figure 1: Jean-Baptiste Joseph Fourier(source wikipedia)

The Fourier Series is a very important mathematics tool discovered by Jean-Baptiste Joseph Fourier in the 18th century. The Fourier series is used in many important areas of science and engineering. They are used to give an analytical approximate description of complex periodic function or series of data.  In this blog, I am going to give a short introduction to it.

Continue reading
Posted in Uncategorized | Leave a comment

Note di Meccanica Classica

In questo blog vengono derivate alcune equazioni fondamentali della meccanica classica che sono anche alla base del metodo della simulazione di Dinamica Molecolare.

Continue reading
Posted in Science Topics, What is new | Leave a comment

La Serie​ di Taylor

La serie di Taylor è un utilissimo strumento matematico. In questo blog, ne darò una breve descrizione dando qualche esempio di applicazione.

Chi è il signor Taylor?

Brook Taylor (1685 – 1731) era un matematico britannico del XVII secolo che ha dimostrato la formula che porta il suo nome, e l’argomento di questo blog, nel volume Methodus Incrementorum Directa et Inversa (1715). Maggiori informazioni si possono trovare nella corrispondente pagina della wikipedia.

Continue reading
Posted in Uncategorized | Leave a comment

The Taylor Series

The Taylor series is a mathematical tool that, sometimes, it is not easy to immediately grasp by freshman students. In this blog, I will give a short review of it giving some examples of applications.

Who is Mr. Taylor?

Brook Taylor (1685 – 1731) was a 17th-century British mathematician. He demonstrated the celebrated Taylor formula, the topics of this blog, in his masterwork Methodus Incrementorum Directa et Inversa (1715). For more information, just give a read to the following wiki page.

Continue reading
Posted in Uncategorized | 2 Comments

Modeling Natural Shapes: Sunflowers Florets and the Golden Ratio

Il girasole piega a occidente
e già precipita il giorno nel suo
occhio in rovina … 
from the poem  “Quasi un madrigale” by Salvatore Quasimodo.

 

Continue reading

Posted in Programming, Science Topics | Leave a comment

Modeling Natural Shapes: Seashells

O conchiglia marina, figlia
della pietra e del mare biancheggiante,
tu meravigli la mente dei fanciulli.

La conchiglia di Alceo. (Traduzione di Salvatore Quasimodo, da Lirici greci, 1940) 

 

Continue reading

Posted in Uncategorized | Leave a comment

Physical Chemistry: The Simple Hückel Method

The Hückel molecular orbital method is a quantum mechanics approach for calculating the energies of molecular orbitals of π electrons in conjugated hydrocarbon systems, such as ethylene, benzene, and butadiene. Continue reading

Posted in Science Topics | Leave a comment