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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/calculus-through-data-and-modelling-differentiation-rules
课程评论：没有评论
课程名称：通过数据与建模学习微积分：微分法则 课程概述： 《通过数据与建模学习微积分：微分法则》继续研究可微分微积分，通过发展新的微分法则，可以在不直接使用极限定义的情况下找到导数。这些微分法则将使得计算变化率变得十分轻松，包括多项式、理性函数、代数函数、指数和对数函数，以及三角和反三角函数的导数。一旦这些法则建立，将应用于解决涉及变化率和函数近似的问题。 课程大纲： 1. **多项式、指数和对数函数的导数**：我们将探讨多项式、指数、对数等重要函数的导数，并学习提高计算导数效率的微分法则，同时将导数的概念推广到多变量函数，并学习如何在空间中的图形上找到导数和变化率。 2. **乘积法则和商法则**：这一部分的公式使我们能够对通过乘法或除法形成的新函数进行微分。 3. **三角函数的导数**：在本模块中，我们会总结三角函数（特别是正弦和余弦）的导数公式。结合乘积和商法则，我们还形成其余三角函数的导数公式并用于变化率相关问题的求解。 4. **链式法则**：许多函数是通过其他函数的组合而形成的。这个模块将发展链式法则，一个在本课程中极为重要的微分法则，帮助我们找到函数复合的导数，具有多种应用。 5. **偏导数**：这一模块将导数的概念应用于多变量函数，讨论偏导数的计算规则及几何解释；工具的多变量推导使得对更复杂数据集的分析成为可能。 6. **方向导数和梯度向量**：在本模块中，我们将继续应用偏导数，找出任意方向的变化率，通过发展方向导数和梯度向量的理论。这些多变量微积分的新工具可以应用到经济学、物理、生物学和数据科学等问题中。 7. **最终项目：飞行路径**：将课程理论应用于建模飞行器的着陆路径。 该课程适合希望深入理解微分法则并将其应用于实际问题的学习者。
Name:Derivatives of Polynomial, Exponential, and Logarithmic Functions
Description:In previous course, we defined and calculated the derivative as a limit. In this module, we will examine the derivatives of some important functions, including polynomials, exponentials, logarithms, and trigonometric functions. We will also learn differentiation rules which will help us to compute derivatives more efficiently. Finally, we will generalize the idea of a derivative to multivariable functions, and learn how to find derivatives and rates of change on a graph in space.
Name:The Product and Quotient Rules
Description:The formulas of this section enable us to differentiate new functions formed from old functions by multiplication or division.
Name:Derivatives of Trigonometric Functions
Description:Before starting this module, please review trigonometric functions, in particular their graphs. In this module, we will develop formulas to find derivatives for the common trigonometric functions of sine and cosine. Together with the product and quotient rules, the derivatives for the remaining trigonometric functions are formulated. These new derivative formulas are then added to our catalog to use and apply to solve problems related to rates of change.
Name:The Chain Rule
Description:Many functions are created through composition of other functions. In this module, one of the most important of the differentiation rules of this course is developed which will allow us to find derivatives of the compositions of functions. This rule is called the chain rule and has a variety of applications.
Name:Partial Derivatives
Description:In this module, the notion of the derivative is applied to multivariable functions through the notion of partial derivatives. Algebraic rules are developed to find partial derivatives of multivariable functions as well as their geometric interpretations. The development of the tools of calculus to multivariable functions allows for further analysis of more complicated data sets.
Name:Directional Derivatives and Gradient Vectors
Description:In this module, we continue the application of partial derivatives to find rates of changes in any direction by developing the theory of directional derivatives and gradient vectors. These new tools of multivariable calculus can then be applied to problems in economics, physics, biology, and data science.
Name:Final Project: Flight Path
Description:Apply the theory of this course to model a flight path for a landing aircraft.
Calculus through Data & Modeling: Differentiation Rules continues the study of differentiable calculus by developing new rules for finding derivatives without having to use the limit definition directly. These differentiation rules will enable the calculation of rates of change with relative ease the derivatives of polynomials, rational functions, algebraic functions, exponential and logarithmic functions, and trigonometric and inverse trigonometric functions. Once these rules are developed, they are then applied to solve problems involving rates of change and the approximation of functions.
