EuropeEurope is a continent comprising the westernmost peninsulas of Eurasia, located entirely in the Northern Hemisphere and mostly in the Eastern Hemisphere. It shares the continental landmass of Afro-Eurasia with both Africa and Asia. It is bordered by the Arctic Ocean to the north, the Atlantic Ocean to the west, the Mediterranean Sea to the south, and Asia to the east. Europe is commonly considered to be separated from Asia by the watershed of the Ural Mountains, the Ural River, the Caspian Sea, the Greater Caucasus, the Black Sea and the waterways of the Turkish Straits.
History of EuropeThe history of Europe is traditionally divided into four time periods: prehistoric Europe (prior to about 800 BC), classical antiquity (800 BC to AD 500), the Middle Ages (AD 500 to AD 1500), and the modern era (since AD 1500). The first early European modern humans appear in the fossil record about 48,000 years ago, during the Paleolithic Era. Settled agriculture marked the Neolithic Era, which spread slowly across Europe from southeast to the north and west.
World War IWorld War I or the First World War, often abbreviated as WWI or WW1, known contemporaneously as the Great War, was a major global conflict lasting from 1914 to 1918. It was fought between two coalitions, the Allies and the Central Powers. Fighting took place throughout Europe, the Middle East, Africa, the Pacific, and parts of Asia. The first decade of the 20th century saw increasing diplomatic tension between the European great powers.
Eastern EuropeEastern Europe is a subregion of the European continent. As a largely ambiguous term, it has a wide range of geopolitical, geographical, ethnic, cultural, and socio-economic connotations. The region stretches from the Ural Mountains in the east to the borders of Poland and Romania. Most definitions include the countries of Belarus, Russia, and Ukraine while less restrictive definitions also include Bulgaria, the Czech Republic, Hungary, Moldova, Poland, Romania, and Slovakia.
Northwestern EuropeNorthwestern Europe, or Northwest Europe, is a loosely defined subregion of Europe, overlapping Northern and Western Europe. The term is used in geographic, history, and military contexts. Geographically, Northwestern Europe is given by some sources as a region which includes Great Britain, Ireland, Belgium, the Netherlands, Luxembourg, Northern France, parts of Germany, Denmark, Norway, Sweden, and Iceland. In some works, Switzerland, Finland, and Austria are also included as part of Northwestern Europe.
Western EuropeWestern Europe is the western region of Europe. The region's extent varies depending on context. The concept of "the West" appeared in Europe in juxtaposition to "the East" and originally applied to the ancient Mediterranean world, the Roman Empire (Western Roman Empire and Eastern Roman Empire), and medieval "Christendom" (Western Christianity and Eastern Christianity). Beginning with the Renaissance and the Age of Discovery, roughly from the 15th century, the concept of Europe as "the West" slowly became distinguished from and eventually replaced the dominant use of "Christendom" as the preferred endonym within the region.
Southern EuropeSouthern Europe is the southern region of Europe. It is also known as Mediterranean Europe, as its geography is marked by the Mediterranean Sea. Definitions of Southern Europe include some or all of these countries and regions: Albania, Andorra, Bosnia and Herzegovina, Bulgaria, Croatia, Cyprus, Turkey (East Thrace), Gibraltar, Greece, Italy, Kosovo, Malta, Monaco, Montenegro, North Macedonia, Portugal, San Marino, Serbia, Slovenia, Southern France, Spain, and Vatican City.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
