我觉得无穷小比形式化的“基于极限（limits-based）”方法直观多了。我最近在重温当年大学的课程资料，不过用的是一本挺有意思的书：Seth Braver 写的《Full Frontal Calculus: An Infinitesimal Approach》。我很喜欢他通俗易懂的写作风格。比起大家熟知的实数，他富有诗意的引言终于让我直观理解了为什么无穷小会这么管用：“然而，通过发展……
I find infinitesimals more intuitive than the formal 'limits-based' approach. I'm currently studying my old degree material but using a fairly interesting book: "Full Frontal Calculus: An Infinitesimal Approach" by Seth Braver. I like his readable style. His poetic intro finally gave me an intuition why infinitesimals might be useful, compared to the good old reals: "Yet, by developing…
Depends what you're looking for. Full Frontal Calculus[0], Intuitive Infinitesimal Calculus[1], and Elementary Calculus[2] are all textbooks on the calculus sequence using an infinitesimal pov. The basic approach is to extend the Real numbers to include infinitesimals…
我觉得无穷小比形式化的“基于极限（limits-based）”方法直观多了。我最近在重温当年大学的课程资料，不过用的是一本挺有意思的书：Seth Braver 写的《Full Frontal Calculus: An Infinitesimal Approach》。我很喜欢他通俗易懂的写作风格。比起大家熟知的实数，他富有诗意的引言终于让我直观理解了为什么无穷小会这么管用：“然而，通过发展……
I find infinitesimals more intuitive than the formal 'limits-based' approach. I'm currently studying my old degree material but using a fairly interesting book: "Full Frontal Calculus: An Infinitesimal Approach" by Seth Braver. I like his readable style. His poetic intro finally gave me an intuition why infinitesimals might be useful, compared to the good old reals: "Yet, by developing…
这取决于你想找什么。《Full Frontal Calculus》[0]、《Intuitive Infinitesimal Calculus》[1] 和《Elementary Calculus》[2] 都是从无穷小视角讲解微积分进阶课程的教材。其基本方法是扩展实数集以包含无穷小……
Depends what you're looking for. Full Frontal Calculus[0], Intuitive Infinitesimal Calculus[1], and Elementary Calculus[2] are all textbooks on the calculus sequence using an infinitesimal pov. The basic approach is to extend the Real numbers to include infinitesimals…