Differentiation of approximately specified functions
Differentiation of approximately specified functions
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DOI：
10.2307/2324275
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发表时间：
1991-11
影响因子：
0.5
通讯作者：
C. Groetsch
中科院分区：
文献类型：
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作者：
C. Groetsch
有经验的涂鸦者知道，一个函数的图形可以紧紧地绕着一个给定的平滑曲线摆动，而不会偏离太远。任何患有晕动病的人都痛苦地意识到，在拥挤的城市交通中，无情的出租车司机可以在低速下完成猛烈的加速和减速。这些例子，一个是几何的，一个是物理的，都是数学事实的表达，即均匀接近的函数不必有均匀接近的导数。从初等微积分中给出了导数极值行为的一个例子
Experienced doodlers know that the graph of a function can wiggle tightly around, while not departing far from, a given smooth curve. And anyone who suffers from motion sickness is painfully aware of the violent accelerations and decelerations a callous cabby can accomplish at low speeds in crowded city traffic. These examples, one geometrical and one physical, are expressions of the mathematical fact that uniformly close functions need not have uniformly close derivatives. An example from elementary calculus of extreme behavior of the derivative is provided by the function