<A>
Differential Calculus: *
The primary objects of study are the derivative of a function & related notions such as the differential, and their applications. The derivative of a function at a chosen input value describes the rate of change of the function near that input value. The process of finding a derivative is called differentiation. Geometrically, the derivative at a point is the slope of the tangent line to the graph of the function at that point, provided that the derivative exists and is defined at that point. For a real-valued function of a single real variable, the derivative of a function at a point generally determines the best linear approximation to the function at that point.
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ABOVE: graph of a function, drawn in black, and a tangent line to that function (in red); the slope of the tangent line equals the derivative of the function at the marked point.
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<B>
Dynastic principles…of age of Louis XIV: *
Until the emergence of "popular sovereignty" dynastic rule meant that international politics & wars revolved around a few families. Louis XIV's famous claim, "L'état, c'est moi" ("I am the state") reflects the importance of the royal figure as the representative of the state. Dynastic legitimacy meant when no male heir survived the death of a king, a bloody succession crises often followed (e.g. The War of the Spanish Succession 1701-1713 and the War of Austrian Succession 1740-1748).
<C>
Euclidean geometry: *
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ABOVE LEFT: An isosceles triangle can be divided into 2 congruent right triangles.
ABOVE RIGHT: notations for a right triangle. For a right triangle the hypothenuse (denoted c) is the longest side opposite the right angle; the legs (a and b) are the two shorter sides adjacent to the right angle; h denotes the altitude for the hypothenuse, while m and n denote the segments into which this altitude divides the hypothenus
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<D>
Egyptian administrative system: *
Egypt was divided into 42 administrative regions called nomes, each governed by a nomarch, accountable to the vizier. Temples served as houses of worship, but were also responsible for collecting & storing the nation's wealth in a system of granaries & treasuries administered by overseers, who redistributed grain & goods. The economy was centrally organized & strictly controlled, using a simple type of barter with a standard sack of grain and a standard denominator called the deben (a weight of roughly 3 oz of silver); workers were paid in grain; prices were fixed across the country & recorded in lists to facilitate trading; grain could be traded for other goods, according to the fixed price list.
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<E>
Classical coinage: *
Coins provided a medium of exchange used by city-states to hire mercenaries & compensate citizens. They were a mobile form of metal resources, a source of revenue as foreign traders had to change their money into the local currency at an exchange rate favourable to the city state and finally the minting of coins gave prestige to the city state itself.
<F>
Categories of the reason: *
Kant believed that the ability of human understanding to think about and know an object is the same as the making of a spoken or written judgment about an object: "Our ability to judge is equivalent to our ability to think.". A judgment is the thought that a thing is known to have a certain quality or attribute. He has 12 categories which allowed for judgement. He believed that the concepts of space & time, cause & effect, and substance are integral to all human experiences and constitute categories by which the mind makes sense of the phenomenal world & by which the mind can come to judgments.
