| 无须极限新微分法 |
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| 引用本文： | 林兟.无须极限新微分法[J].数学的实践与认识,2000,30(2):245-250. |
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| 作者姓名： | 林兟 |
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| 作者单位： | 浙江大学数学系,杭州,310027 |
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| 摘 要： | 本文摆脱传统的除法 ,以括代除 ,无须极限也能求出切线 ,作出定理 A.由此微积分完全改观 .这是依靠实数有序“无漏”,建立强无穷小ω(Δx) ,取代ε-δ,实质又相互等价 ,作出定理 B.由ω(Δx)定义无穷小与连续 ,由连续再作极限更为自然 .聚点是极限的初步 ,大可发挥 .
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| 关 键 词： | 满严增 (强)无穷小 “ω箭头条件” 本身聚点与漏缺聚点 |
| 修稿时间： | 1998-04-09 |
An easy Method of Differentiation in no need of Limit |
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| LIN Xin.An easy Method of Differentiation in no need of Limit[J].Mathematics in Practice and Theory,2000,30(2):245-250. |
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| Authors: | LIN Xin |
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| Abstract: | Division △y/△x may be simplified by taking out the factor △x without limit, and we can also get the tangent line in theorem A, which gives the differential, its coefficicent gives the derivative. We construct the strong infinitesimal ω(△x) in real number to replace ε-δ. |
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| Keywords: | strictly increasing onto mapping strong infinitesimal ω(△x) ″ ω arrow condition″ accumulation point |
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