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所在平台: Udemy |
课程主页: https://www.udemy.com/course/fourier-and-laplace-transforms/
课程评论：没有评论
Coursera 课程：傅里叶变换与拉普拉斯变换 本课程是傅里叶变换与拉普拉斯变换的入门介绍。课程结合了 Matlab 模拟和在线图形计算器，从几何角度直观地讲解主题，同时也提供严谨的数学阐述。 **核心特色：** * **直观性:** * 通过 Matlab 模拟和在线图形计算器，从几何角度建立直观理解。 * 采用三维图形化方法分解方程，帮助观众构建对数学原理的直观认知。 * **数学严谨性:** * 在直观方法的基础上，提供扎实的数学理论支撑。 * 深入剖析各种与傅里叶变换和拉普拉斯变换相关的概念，例如：傅里叶变换 (FT)、离散时间傅里叶变换 (DTFT)、离散频率傅里叶变换 (DFFT)、离散时间和频率傅里叶变换 (DTFFT)、离散傅里叶变换 (DFT)、快速傅里叶变换 (FFT)，以及拉普拉斯变换的离散形式（Z 变换）。 * **深度理解:** * 旨在帮助学习者深刻理解各种变换的来源及其相互关系。 * 强调对数学核心的深入探究，而非实际应用。 * 适合那些渴望真正理解这一数学领域精髓的学习者。 **课程目标：** 通过本课程，学习者将能够： * 建立对傅里叶变换和拉普拉斯变换的直观理解。 * 掌握相关的数学理论和概念。 * 理解各种离散变换与连续变换之间的联系。 **学习建议：** 课程部分内容具有一定挑战性，需要仔细思考和投入时间。课程提供了英文以及78种语言的字幕。学习者通过对数学原理的深入理解，将获得丰厚回报。 **课程定位：** 本课程侧重于数学方法的理论理解，而非实际编程实现。适合希望深入探究数学“引擎”如何运作的学习者。
This course is an introduction to the Fourier and Laplace Transforms. I introduce this subject both geometrically to give a good intuition using Matlab simulations and an online graphical calculator and also in a more formal mathematical way. The equations are broken down into small elements and an intuitive 3 dimensional graphical method is used in order to build intuition and finally understanding of the mathematics. This 3D intuitive learning approach is also backed up by some solid mathematics. This course has been created in order to give you a core understanding of the methods of mathematical transforms. Some sections are quite advanced and some real thinking is required. Your time and dedication will be rewarded with a deeper understanding of this beautiful subject. Subtitles manually updated in English and converted to 78 different languages.I can assure you that if you are willing to take the time to comprehend the mathematics then the effort will be rewarded ten fold. For example , Fourier Transform (FT) , Discrete Time Fourier Transform (DTFT) , Discrete Frequency Fourier Transform (DFFT) , Discrete Time and Frequency Fourier Transform (DTFFT) , the Discrete Fourier Transform (DFT), the Fast Fourier Transform (FFT) , discrete versions of the Laplace Transform (Z-transform). How are they all related ? By the end of this course you will understand where they all come from and how they are all related to one another. This is not a course about the practical implementation of transforms. This course is about understanding the core subject at a deeper mathematical level. This course is for those who want to truly understand this subject. If you want a new shiny car just to drive then this is not the course for you. If you want to open up the bonnet and take the engine apart to see how it works then this is definitely the course for you.
