In this book, exercises are carried out regarding the following mathematical topics:solving first-order partial-derivative differential equationssolving second-order partial derivative differential equations: elliptic, parabolic and hyperbolicweak problem formulationInitial theoretical hints are also presented to make the conduct of the exercises understandable.

"Decalogue", which aired at the end of 1988, immediately became a cornerstone of Krzysztof Kieślowski's artistic work and, more generally, of cinematography.This book will present the meanings and themes exposed, the various levels of interpretation and symbolism, the connections and references, the stylistic choices and the history that led to the conception and creation of the late director's Polish symbolic work

This manual explains the fundamental concepts for understanding natural gas pricesIn particular, the following topics are covered:what is natural gas, what are the reference markets and prices, what are the fundamentals of gas based on production, consumption, exports and stocks, what influences the price and insights into the financial instruments available. The obvious and obvious conclusion will be that natural gas is a very particular raw material with peculiarities not f...

The following topics are presented in this book:introduction to waves and their propertiesacoustic waveshuman acoustics and phonometric systemsroom acoustics and hints of building acoustic design

The eighteenth century began with the absolutism of the Sun King and the pervasive presence of empires like the English and Russian, and ended with the figures of Napoleon and the independence of the United States of America.This transformation was made possible by three distinct, and almost simultaneous, revolutions: the American, the French, and the Industrial Revolution.These revolutions were based on two solid pillars: the Enlightenment, which owed much of its foundation ...

The great power of human culture and knowledge, expressed in multiple aspects of daily life and speculative reflection, did not seem sufficient to stem the violence of arms and the prevalence of war in a century, the eighth, which saw the peak of the Islamic Caliphate and the Lombard kingdom's expansion, while an intense unifying drive attempted to create a new Empire after centuries of fragmentation.This dichotomy underpinned the triple vicissitudes of various families who, from on...

Three distinct portraits of tenth-century life unfold chronologically, from the Heian era in Japan, marked by the rise of the Fujiwara clan, to the rebirth of the Holy Roman Empire under Otto I of Saxony, and finally to the Viking spirit of adventure that reached the farthest reaches of northern Iceland and Greenland.Amid these events, several families of middle and lower social standing operate, each with their own desire for greatness and expansion, leveraging the qualities and ta...

The century marking the transition from the Middle Ages to the modern era opens with a feudal legacy stemming from the internal divisions of France and England, still embroiled in the Hundred Years' War.Between mutual betrayals and the mystical figure of Joan of Arc, this historical transition marks the arrival of gunpowder in Europe, marking one of the world's epochal changes.Along with it, the invention of movable type printing and the fall of the Eastern Empire pave the wa...

As the eleventh century unfolded, the clash of civilizations became increasingly evident.Starting from the great cultural and enlightened era associated with the studies of Ibn Sina, under the Shiite Islamic dynasty of the Buwayhids, destined to succumb to the blows of the Seljuks, the story moves to Normandy, following the vicissitudes of the battles in France and then in England during the reign of William the Conqueror.The century ended with a blaze of violence, unleashed ...

The fragmentation of the Holy Roman Empire due to internal struggles among Charlemagne's heirs and the arrival of Norman history marked the unfolding of events in the ninth century, through a relentless succession of hopes and immediate disillusionments regarding a past that was not destined to repeat itself.At the same time, the individual families belonging to these peoples tended to follow events, following the decisions of others. The Empire crumbled, and with it, the history of...

The travails of the third century, characterized by a profound social crisis in the Roman Empire, shaken by civil wars and constant invasions, inevitably affected the Italian family, beginning with the descendants of Numa, the imperial legate who won countless battles and would be the last witness of the Severan dynasty.In the darkest period of Rome's thousand-year history, amid usurpers and the end of patrician rule, there were key figures capable of averting collapse and restoring...

The eternal cycle of Life, made up of births and rebirths, is the protagonist of a series of circular stories, completely detached from a precise spatial and temporal location.Suspended between being unique or connected to other people, the different dialectics, allegorically represented by as many female figures, bring out the evidence of being and becoming, in an endless dance that involves every single person.