|
所在平台: Udemy |
课程主页: https://www.udemy.com/course/upgrade-university-calc-1-limits-derivatives/
课程评论：没有评论
《Calc 1: Limits & Derivatives》是Coursera上的一门微积分入门课程，主要涵盖两大核心概念：极限与导数。 **极限** 部分将探讨函数在某一点附近的“行为”，即当输入值趋近于特定值时，函数的输出值如何变化。课程将深入分析“接近”的数学含义，以及如何利用函数的连贯性来理解其在某个区间上的性质，例如平滑性。此外，还将研究诸如“除以零”的附近情况以及如何结合极限与斜率的代数方程来确定曲线的斜率。 **导数** 部分则将介绍导数作为描述函数斜率的工具。课程将引导学习者理解如何计算非直线斜率，以及如何利用不同基本运算的规则来简化导数的计算。还将探讨导数为零的意义，多相关函数导数之间的关系，以及连续求导（求二阶导数等）的概念。 完成本课程将为学习者打开数学新领域的大门，并培养一种全新的数学思维方式。
A typical calculus 1 course covers two main topics: limits and derivatives.Limits describe what happens to a function near a specific point (but not necessarily at that point). The intimately-related topic of continuity is perhaps the most important underpinning of theorems about functions. You'll learn how to think about questions like:What does it mean to be "close" to a point?What can we learn about a function on an interval given that the curve is connected? Smooth?How do we know what happens in the neighborhood of dividing by zero?How can we combine limits and the algebra equation for slope to think about the slope of a curve?Derivatives are functions which describe the slope of a corresponding function. Once we can think about the behavior of the derivative, a whole range of applications present themselves! You'll learn how to think about questions like:How do we evaluate the slope of a line that isn't straight?What simplifications can we use in evaluating derivatives based on the different types of basic operations?What does it mean for the slope to be zero?How do derivatives of multiple related functions interrelate?What happens if you take the derivative of the derivative?Can't wait to get started! Calculus 1 is a gateway into a whole new realm of math and way of thinking. Let's go!
