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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/differentiation-calculus
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课程名称：微积分：单变量第2部分 - 微分 课程概述：微积分是人类思维的伟大成就之一，它解释了从行星轨道到城市最佳规模再到心跳周期等诸多现象。本课程快速覆盖了单变量微积分的核心思想，着重于概念理解和应用，适合工程、自然科学和社会科学的初学者。该课程的显著特点包括：1）从一开始就引入并使用泰勒级数和近似；2）将离散和连续微积分形式的创新综合；3）强调概念而非计算；4）提供清晰、动态的统一方法。 在这第二部分（五部分中的第二部分），我们将探讨导数、微分法则、线性化、高阶导数、优化、微分和微分算子等内容。 课程大纲： 1. 新视角看微分： 描述：我们将重新思考导数的定义和其意义，利用上章的渐进（或大-O）符号。这将为描述和理解变化率及相关规则提供新的语言。 2. 将导数运用到实践： 描述：导数为何在微积分中如此重要？部分原因是它们的广泛应用！在此模块中，我们将回顾导数的一些核心应用，展示理解渐进性如何帮助建立导数应用。 3. 微分与算子： 描述：导数不仅仅涉及计算和应用。导数的另一面在于微分的神秘表现形式。这些微分源于隐式微分，揭示了对微分更深层次的理解。
Name:A New Look at Differentiation
Description:Think derivatives mean "slopes"? Not anymore... In this module, we will reconsider what a derivative is and means in terms of the asymptotic (or big-O) notation from the previous chapter. This will give us a new language for describing and understanding rates of change and the rules that govern them.
Name:Putting Derivatives to Work
Description:Why exactly are derivatives so central to calculus? In part, it is because they are so ubiquitously useful! In this module, we will recall a few core applications of derivatives. In so doing, we'll see exactly how having an understanding of the asymptotics assists in building applications of the derivative.
Name:Differentials and Operators
Description:There is much more to derivatives than simply their computation and applications. So much of how they arise is calculus is in the mysterious guise of *differentials*. These arise from implicit differentiation, which in turn reveals a deeper level of understanding of what differentiation means.
Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach. In this second part--part two of five--we cover derivatives, differentiation rules, linearization, higher derivatives, optimization, differentials, and differentiation operators.
