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所在平台: Udemy |
课程主页: https://www.udemy.com/course/calculus-complete-course/
课程评论：没有评论
课程名称：微积分：完整课程 课程概述：该课程旨在带领学生从初学者成长为微积分专家，内容设计既有趣又富有互动性，充满示例和解释，适合任何希望以严格却直观且愉快的方式学习微积分的人。课程涵盖的概念是许多其他学科的核心，例如机器学习、数据科学、工程、物理学及财务分析等。视频中包含大量详细的示例和解释，确保学员不会迷失方向，许多主题还在免费的图形软件Geogebra中得以实现。 课程关键内容包括： - 微分基本技能：了解微分的定义，及其在寻找梯度、极大值和极小值点，以及解决优化问题中的应用。 - 积分基本技能：学习积分的定义及其在计算曲线下和曲线之间的面积中的应用。 - 微分方法：链式法则、乘积法则、商法则等。 - 积分方法：按替换积分、分部积分及其他多种高级技巧。 - 微分的应用：洛必达法则、牛顿法、麦克劳林级数和泰勒级数。 - 积分的应用：旋转体体积、表面积和弧长。 - 替代坐标系统：参数方程和极坐标曲线。 - 一阶微分方程：学习一系列技巧，包括变量分离和积分因子。 - 二阶微分方程：学习解决齐次和非齐次微分方程以及耦合和可约微分方程的方法。 课程要求具备扎实的代数基础，为了顺利通过前几章，理解三角函数、指数和对数是有帮助的，尽管我将对每个主题进行简要介绍。 请注意：此课程与美国的Calc 1、Calc 2和Calc 3课程无关，也不是为了特定准备这些课程而设计的。虽然对有意向学习这些课程的学生很有帮助，但这并不是本课程的目标。
This is course designed to take you from beginner to expert in calculus. It is designed to be fun, hands on and full of examples and explanations. It is suitable for anyone who wants to learn calculus in a rigorous yet intuitive and enjoyable way.The concepts covered in the course lie at the heart of other disciples, like machine learning, data science, engineering, physics, financial analysis and more.Videos packed with worked examples and explanations so you never get lost, and many of the topics covered are implemented in Geogebra, a free graphing software package.Key concepts taught in the course are:Differentiation Key Skills: learn what it is, and how to use it to find gradients, maximum and minimum points, and solve optimisation problems.Integration Key Skills: learn what it is, and how to use it to find areas under and between curves.Methods in Differentiation: The Chain Rule, Product Rule, Quotient Rule and more.Methods in Integration: Integration by substitution, by parts, and many more advanced techniques.Applications of Differentiation: L'Hopital's rule, Newton's method, Maclaurin and Taylor series.Applications in Integration: Volumes of revolution, surface areas and arc lengths.Alternative Coordinate Systems: parametric equations and polar curves.1st Order Differential Equations: learn a range of techniques, including separation of variables and integrating factors.2nd Order Differential Equations: learn how to solve homogeneous and non-homogeneous differential equations as well as coupled and reducible differential equations.Much, much more!The course requires a solid understanding of algebra. In order to progress past the first few chapters, an understanding of trigonometry, exponentials and logarithms is useful, though I give a brief introduction to each.Please note: This course is not linked to the US syllabus Calc 1, Calc 2 & Calc 3 courses, and not designed to prepare you specifically for these. The course will be helpful for students working towards these, but that's not the aim of this course.
