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所在平台: Udemy |
课程主页: https://www.udemy.com/course/a-complete-guide-to-1st-order-ordinary-differential-equation/
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课程名称：《一阶常微分方程完全指南》 课程概述： 本课程旨在介绍一阶常微分方程（ODE）的基本概念和应用，涵盖微分方程的分类、初值问题及其作为数学模型的应用。微分方程在包括人口动态、连续复利、系列电路和物体运动等多个实际生活中有着广泛的应用。 课程结构包括以下几个部分： 1. **预备知识**： - 微分方程的分类（类型、阶数和线性） - 可分离变量 - 初值问题（IVP） 2. **作为数学模型的一阶微分方程**： - 模型I：与依赖变量成比例 - 模型II：与一个界限的差异成比例 - 模型III：逻辑斯蒂方程 - 五个人口模型 - 模型IV：一阶线性ODE - 应用实例：混合问题、系列电路、运动数学模型、托里切利法则 3. **一阶ODE求解方法**： - 可分离变量 - 一阶线性ODE - 齐次一阶ODE - 精确一阶方程 - 使用积分因子使方程精确 - 伯努利方程 - 通过替代法求解 课程包含丰富的学习内容： - **视频讲解**：每个主题由讲师介绍和解释，提供解题技巧和示例。 - **讲义笔记**：课程中的讲义可供下载，方便离线复习。 - **作业练习**：课程中将提供作业以强化学习，鼓励学员在查看解答前先自行尝试解决问题。 课程还提供了讲师对学员成功的关注、终身访问权限及以下亮点： - 可下载的讲座视频，支持随时随地观看。 - 可下载的讲义，方便不使用设备时复习。 - 在第3和第4部分末尾提供两套带解答的练习题，帮助展现所学知识。 通过这门课程，您将全面掌握一阶常微分方程及其实际应用，期待在课程中与您见面！- Gina Chou
HOW THIS COURSE WORK:Differential Equations (DE) are equations that contain derivatives of one or more dependent variables with respect to one or more independent variables. DEs have many real-life applications. For example, population dynamics, continuous compound interest, series circuits, motion of a particle, and more.This course, A Complete Guide to First-Order Ordinary Differential Equation, includes the first two sections of my complete course on ODE, including video, notes from whiteboard during lectures, and practice problems (with solutions!). I also show every single step in examples and proofs. The course is organized into the following topics:Section 2: PreliminariesClassification of DEs (type, order, and linearity)Variables SeparableInitial-Value Problems (IVP)Section 3: First-Order ODEs as Mathematical ModelsModel I: Proportional to the Dependent VariableModel II: Proportional to the Difference to a BoundModel III: The Logistic EquationFive Population ModelsModel IV: First-Order Linear ODEApplication: A Mixture ProblemApplication: Series CircuitsApplication: Mathematical Models Describing MotionTorricelli's LawSection 4: First-Order ODEs' Methods of SolutionVariables SeparableFirst-Order Linear ODEHomogeneous First-Order ODEExact First-Order EquationMaking an Equation Exact by an Integrating FactorBernoulli's EquationSolving by SubstitutionsSection 5: Second Order Equations and Linear Equations of Higher Order (Available in the complete course)Section 6: Laplace Transforms (Available in the complete course)Section 7: Linear Systems of ODEs (Available in the complete course)CONTENT YOU WILL GET INSIDE EACH SECTION:Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issue you may encounter in class and make sure you can solve any problem by yourself.Notes: In each section, you will find my notes as downloadable resource that I wrote during lectures. So you can review the notes even when you don't have internet access (but I encourage you to take your own notes while taking the course!).Assignments: After you watch me doing some examples, now it's your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again.THINGS THAT ARE INCLUDED IN THE COURSE:An instructor who truly cares about your successLifetime access to A Complete Guide to First-Order Ordinary Differential EquationHIGHLIGHTS:#1: Downloadable lectures so you can watch the videos whenever and wherever you are.#2: Downloadable lecture notes so you can review the lectures without having a device to watch/listen.#3: Two problem sets at the end of Sections 3 and 4 (with solutions!) for you to do more practice.#4: Step-by-step guide to help you solve problems.See you inside the course!- Gina Chou:)
