108 books
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9 voters
Calculus
Calculus (from Latin calculus, literally "small pebble used for counting on an abacus") is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of co
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Yet in another way, calculus is fundamentally naive, almost childish in its optimism. Experience teaches us that change can be sudden, discontinuous, and wrenching. Calculus draws its power by refusing to see that. It insists on a world without accidents, where one thing leads logically to another. Give me the initial conditions and the law of motion, and with calculus I can predict the future -- or better yet, reconstruct the past. I wish I could do that now.
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― The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math
― The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math
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Cournot protested that concepts exist in the understanding, independently of the definition which one gives to them. Simple ideas sometimes have complicated definitions, or even none. For this reason he felt that one should not subordinate the precision of such ideas as those of speed or the infinitely small to logical definition. This point of view is diametrically opposed to that which analysis since the time of Cournot has been toward ever-greater care in the formal logical elaboration of the
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― The History of the Calculus and Its Conceptual Development
― The History of the Calculus and Its Conceptual Development
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