RomandyRomandy (Romandie or Suisse romande) is the French-speaking part of Switzerland. In 2020, about 2 million people, or 22.8% of the Swiss population, lived in Romandy. The majority of the romand population lives in the western part of the country, especially the Arc Lémanique region along Lake Geneva, connecting Geneva, Vaud and the Lower Valais. French is the sole official language in four Swiss cantons: Geneva, Vaud, Neuchâtel, and Jura. Additionally, French and German have co-official status in three cantons: Fribourg/Freiburg, Valais/Wallis, and Berne/Bern.
ValaisValais (UKˈvæleɪ , USvæˈleɪ , valɛ; Valês; Wallis ˈvalɪs), more formally the Canton of Valais, is one of the 26 cantons forming the Swiss Confederation. It is composed of thirteen districts and its capital and largest city is Sion. The flag of the canton is made of thirteen stars representing the districts, on a white-red background. Valais is situated in the southwestern part of the country. It borders the cantons of Vaud and Bern to the north, the cantons of Uri and Ticino to the east, as well as Italy to the south and France to the west.
Franco-ProvençalFranco-Provençal (also Francoprovençal, Patois or Arpitan) is a language within Gallo-Romance originally spoken in east-central France, western Switzerland and northwestern Italy. Franco-Provençal has several distinct dialects and is separate from but closely related to neighbouring Romance dialects (the langues d'oïl and the langues d'oc, in France, as well as Rhaeto-Romance in Switzerland and Italy). Even with all its distinct dialects counted together, the number of Franco-Provençal speakers has been declining significantly and steadily.
LausanneLausanne (loʊˈzæn , USalsoloʊˈzɑːn , lɔzan; Losena lɔˈzəna) is the capital and largest city of the Swiss French-speaking canton of Vaud. It is a hilly city situated on the shores of Lake Geneva, about halfway between the Jura Mountains and the Alps, and facing the French town of Évian-les-Bains across the lake. Lausanne is located northeast of Geneva, the nearest major city. The municipality of Lausanne has a population of about 140,000, making it the fourth largest city in Switzerland after Basel, Geneva, and Zurich, with the entire agglomeration area having about 420,000 inhabitants (as of January 2019).
NyonNyon (njɔ̃; historically German: Neuis or Neuss and Italian: Nione, ˈnjone) is a municipality in Nyon District in the canton of Vaud in Switzerland. It is located some 25 kilometers north east of Geneva's city centre, and since the 1970s it has become part of the Geneva metropolitan area. It lies on the shores of Lake Geneva and is the seat of Nyon District. The town has () a population of and is famous in the sporting world for being the headquarters of the Union of European Football Associations (UEFA) and the European Club Association (ECA).
Finite differenceA finite difference is a mathematical expression of the form f (x + b) − f (x + a). If a finite difference is divided by b − a, one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. The difference operator, commonly denoted is the operator that maps a function f to the function defined by A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives.
Difference quotientIn single-variable calculus, the difference quotient is usually the name for the expression which when taken to the limit as h approaches 0 gives the derivative of the function f. The name of the expression stems from the fact that it is the quotient of the difference of values of the function by the difference of the corresponding values of its argument (the latter is (x + h) - x = h in this case). The difference quotient is a measure of the average rate of change of the function over an interval (in this case, an interval of length h).
