Applied Calculus with Python

所在平台: Coursera

课程主页: https://www.coursera.org/learn/applied-calculus-with-python

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课程简介

课程名称：使用 Python 的应用微积分 课程概述：本课程专为希望打下微积分基础的 Python 程序员以及希望学习微积分理论和数值技术的数学学生而设计。课程的目标是通过 Python 开发强大的应用程序，解决各种现实世界中的挑战。课程包括视频讲座、阅读资料、实例、评估和 Python 代码，帮助学生理解如何解决方程、处理函数以及计算和应用导数与积分。如果你对应用数学、数据科学、网络安全或人工智能等领域感兴趣，或者只是想复习微积分或 Python 编程，这门课程将非常适合你。 课程大纲： 1. **Python 入门**：学生将学习使用 Python 编程，并运用这些技能来解决实际复杂问题，通过大量示例和解释促进理解。鼓励学生进行独立实验，完成与模块相关的作业，以解决科学问题并增强挑战感。 2. **函数**：介绍函数的理论与图形，探讨量与量之间的依赖关系，学习如何在 Python 中实现这些函数。 3. **变化率与导数**：讲解微积分的基本概念，尤其是如何通过极限来开发函数的导数以及如何在 Python 中找到导数。 4. **导数法则与应用**：发展导数的计算法则，帮助理解导数的性质，掌握处理复杂函数的技巧。 5. **累积变化与积分**：探讨积分微积分，学习如何通过将小区域相加来求得面积或体积，并运用基本微积分定理将积分与导数联系起来，配合 Python 进行数值计算。 这个课程将使学生掌握核心的微积分概念，能够使用 Python 开发能够解决各类实际问题的应用程序。

课程大纲

Name:Introduction to Python

Description:Programming now has relevance well beyond just Computer Science. In this module and throughout this course, you will learn not only about programming using Python, but also how to use those skills to solve real, complex problems in future classes, at work, or elsewhere. To ensure this, copious amounts of examples are included, with explanations, throughout the course. You are strongly encouraged not only trace through them, but also experiment with (run, alter, break) them on your own. The assignments are linked to the respective module. Putting time in here will give you the opportunity to solve actual scientific problems and challenge you in a way that that’ll not only help you make use of the skills we’ll discuss in lecture, but also to leave you with that oh-so-satisfying feeling of having conquered the challenge when you’re done!

Name:Functions

Description:Functions arise whenever one quantity depends on another. Mathematically speaking, a function is a rule that assigns to each element x in a set D (called the domain) exactly one element, called f(x), in a set called the range. Because we continually make theories about dependencies between quantities in nature and society, functions are important tools in the construction of mathematical models. In this module, we will learn the theory of functions, see many examples and their graphs, as well as apply these functions. We will learn how to implement these functions in Python as well.

Name:Rates of Change and the Derivative

Description:Calculus is the science of measuring change. Early in its history, its tools were developed to solve problems involving the position, velocity, and acceleration of moving objects. Prior to the development of calculus, there was no way to express this change in a variable. In this section, we introduce the notion of limits to develop the derivative of a function. The derivative, commonly denoted as f'(x), will measure the instantaneous rate of change of a function at a certain point x = a. This number f'(a), when defined, will be graphically represented as the slope of the tangent line to a curve. We will see in this module how to find limits and derivatives both analytically and using Python.

Name:Derivative Rules and Applications

Description:The derivative is defined as a limit of the difference quotient. Computing this limit symbolically is very challenging for complicated functions. In this section, we develop rules that find the derivative without having to fall back on the limit definition each time. These rules are purely algebraic in nature and help us gain intuition into the behavior of a derivative function. More importantly, these rules help to demystify the Derivative() function and show the steps to produce the functions output. Understanding the process allows for mastery, adaptation, and more complicated applications of these concepts.

Name:Accumulated Change and Integrals

Description:One major topic in calculus is what is called "integral calculus," which involves finding areas or volumes of regions by adding up small slices. We start to think about areas or volumes as an accumulation of the smaller slices that make them and from that we can apply the theory of integral calculus to measure net change and total accumulations. Then, by the Fundamental Theorem of Calculus, this is then related back to where we started: derivatives. This module introduces some of the most beautiful and useful applications of calculus. Algebraic techniques will be shown alongside of numerical computations using Python.

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