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所在平台: Udemy |
课程主页: https://www.udemy.com/course/differential-calculus-for-physicists/
课程评论：没有评论
Coursera 课程“物理学微分学”概述： 本课程将带您深入了解微分学的核心概念，特别关注其在物理学中的应用。您将首先学习平均增长率（或平均变化率）及其与瞬时增长率（或变化率）的区别。 课程将通过一个关于一个生长速度极快的“奇怪婴儿”的有趣案例，生动地介绍如何通过导数来计算变化率。在此基础上，您将学习一系列用于计算更复杂导数的规则，其中链式法则（Chain Rule）将是重点讲解的内容。讲师提供了大量链式法则的解题实例，以期提供最大的清晰度。 此外，课程还会介绍如何利用对数（Logarithms）来简化某些导数运算，以及处理隐函数微分（Implicit Differentiation）的技巧，因为这种情况在许多物理学主题中频繁出现。 在整个学习过程中，您将接触到大量运用不同求导规则的例题。最终，课程将引出导数的几何意义，以及如何利用导数解决有关最大值（maxima）和最小值（minima）的问题。导数的几何意义在物理学中有着广泛的应用，尤其是在运动学（Kinematics）或力学（Mechanics）的图表中。当遇到“最大”、“最小”、“至少”、“最大”等词语时，微积分提供了一种强大且常常是唯一有效的解决问题的方法。
You will learn what is average growth rate (or average rate of change) and its difference from growth rate (or rate of change). You will be introduced to calculating growth rate (also called derivative) using a very interesting example of a very strange baby growing at an exceedingly fast rate. Also you will be introduced to the different rules to calculate more complicated derivatives with the chain rule being the most complex one among them. I have solved lots of problems involving chain rule to give maximum clarity to you. Also some of the problems have been solved using logarithms which makes solving quite easy in some situations. A few problems involving implicit differentiation also have been solved as such situations may often occur in many topics.You will be seeing a lot of problems being solved in these lectures using different rules of derivatives and finally introduced to the concepts of geometrical meaning, maxima and minima and problems pertaining to them. The geometrical meaning of derivative is one of the most widely used concepts particularly in areas of physics like graphs in kinematics (or Mechanics). Also when we encounter words like maximum, minimum, least, greatest etc one of the most popular ways of solving such problems is calculus. Sometimes the calculus route may be the only way to solve such problems.
