# Berechnung der Konstante von Madelung

Die gesamte Coulomb-Potentialenergie eines Kristalls ist die Summe der einzelnen Terme der elektrostatischen Potentialenergie

$\displaystyle V_{AB} = \frac{e^2}{4\pi\epsilon_0} \frac{Z_AZ_B}{r_{AB}} \hfill (1)$

zum Laden von Ionen  ${q_A}$ e ${q_B}$ und  getrennt nach Entfernung ${r_{AB}}$.

Die Summe erstreckt sich auf alle im Festkörper vorhandenen Ionenpaare für alle kristallinen Strukturen.

Die Summe konvergiert sehr langsam, weil die ersten Nachbarn des Zentralatoms einen substanziellen Beitrag zur Summe mit einem negativen Term liefern, während die benachbarten Sekunden nur mit einem etwas weicheren positiven Term beitragen, und so weiter. Auf diese Weise wird der Gesamteffekt sicherstellen, dass eine totale Initation der Anziehung zwischen Kationen und Anionen vorherrscht mit einem (negativen) Beitrag, der für die Gesamtenergie günstig ist.

# Frosinone and the Ciociaria

Glie musèu  Tra glie campanìle i l'Annunziàta,'Ntòcce prima della uìa ‘Ngelòne,Stamatìna sò fatte 'na fermàtaPè rattaccà le strengh'a strucenòne. Me uànne gli'òcchie doppe 'na utràtaI uède, tutt'a giòrne, nè salòneAddò 'na raccòta sta urdenàtaDe prete, crete, pièzze de matòne, Cule de uàse, de pile, de pignàte,Màneche de recciòle i de bicchièraAncòra prima de Nuè 'mpastàte. Quante sècule,frà, che sò passàte'Nche gli'Ome a trebbulà 'ncim'a sta TeraI ch'è remàste ? Ddù cocce smenuzzàte.               Irèno Da Vialìra (Poeta ciociaro)

I am European of Italian nationality. I very proud of my background but, unfortunately, my carrier put me in an orbit that does intersect my country only during my holiday vacations. In these close encounters, my landing site is Frosinone. When not-Italian acquaintances want to know about my Heimat, most of them are puzzled about the name and location of my hometown. Usually, I help them to overcome the understandable disorientation by giving as reference Rome and telling them that my birthplace is somewhere 80 km in the South of the Caput Mundi. Last year (2018) my hometown soccer team (Frosinone Calcio, nicknamed Canarini, The Canaries, for their home colours)) moved in the first league (A) of the national soccer championship. So, let see if this success will help to raise its notoriety!

It is a long time that I would like to write about Frosinone. However, in this article, I won’t write about the success of the Canarini football team but about my hometown and the rural place in central Italy where it is located.

In the province of Frosinone, there are many historical famous towns such as Anagni that has the exquisite Anagni Cathedral with its museum, Alatri with its megalitic Acropolis, Ferentino another megalytic city with also a beutyful Romanesque Duomo, Veroli and the closeby Certosa of Trisulti that has been recently on news spot for the sadly attempt to trasform this wolderful medieval santuary of christianity and culture to a private business when instead it should be preserved and nominated instead as an humanity heritage. I will talk about these town in other articles. This just to mention some of the famous towns and cultural places in Ciociaria.

# Calculus in a Nutshell: Functions and their Derivatives

When I was about thirteen, the library was going to get ‘Calculus for the Practical Man.’ By this time I knew, from reading the encyclopedia, that calculus was an important and interesting subject, and I ought to learn it.

Richard P. Feynman, from What Do You Care What Other People Think?

## Introduction

Calculus is an important branch of mathematics that deals with the methods for calculating derivatives and integrals of functions and using this information to study the properties of functions. It was independently invented by I. Newton and W. Leibniz in the 18${^{th}}$ century and it was further developed by other great mathematicians in the centuries that follows (see Figure below).

It comprises two areas:

• Differential calculus ${\rightarrow}$ It concerns the study of the rate of variation of functions.
• Integral calculus ${\rightarrow}$ It concern the study of the area under functions.

Depending on the nature of the functions involved in the calculations, we can further distinguish between the single- and multi-variable calculus. In this chapter, the main concepts and methods of the single-variable calculus are summarised.

# 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).

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.