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所在平台: Udemy |
课程主页: https://www.udemy.com/course/ace-ordinary-differential-equations-in-17-hours/
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课程名称：17小时掌握常微分方程 课程概述：本课程旨在介绍常微分方程（DE）的基本概念及其在现实生活中的应用，包括种群动态、连续复利、串联电路和粒子运动等。课程内容包括视频讲座、白板笔记以及提供解决方案的练习题，帮助学生理解并解决涉及变化率的实际问题。每个例子和证明的每一步都将详细展示。 主要内容包括： - **前置知识**：DE的分类（类型、阶次和线性），可分离变量，初值问题（IVP） - **一阶微分方程作为数学模型**：包括与依赖变量成比例的模型、界限差值模型、逻辑斯蒂方程及人口模型等 - **一阶微分方程的解法**：可分离变量、一阶线性微分方程、齐次方程、精确方程及伯努利方程 - **二阶及高阶线性方程**：包括初值及边值问题、齐次与非齐次DE以及常系数下的组合解法 - **拉普拉斯变换**：基本函数的变换及其导数与积分的变换 - **线性微分方程组**：齐次与非齐次线性系统的解法 课程结构还包括： - **视频讲解**：每个主题由讲师开场，详细解释概念和问题解决技巧 - **笔记下载**：每节课提供讲师的课后笔记，方便离线复习 - **作业练习**：每完成一节课后，将有配套的作业，帮助巩固知识 课程亮点： 1. 终身访问完整课程 2. 可下载的课程视频和讲义 3. 每个章节的五套练习题及解决方案 4. 步步引导的解题技巧 欢迎加入课程，开启你的常微分方程学习之旅！——Gina
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, Ace Ordinary Differential Equations in 17 Hours, is intended to introduce students to construct and solve real-life problems involving the rate of change of some quantity. The course includes 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 OrderSecond-Order with Dependent or Independent Variable MissingInitial-Value Problem and Boundary-Value ProblemHomogeneous vs. Nonhomogeneous DEsComplementary Function, Particular Solution, and General SolutionSuperposition PrincipleLinear Independence of FunctionsReduction of OrderHomogeneous Linear ODE with Constant CoefficientsHomogeneous Cauchy-Euler EquationUndetermined CoefficientsVariation of ParametersGreen's FunctionSection 6: Laplace TransformsGamma FunctionTransforms of Some Basic FunctionsTransforms of DerivativesTransforms of IntegralsDerivatives of TransformsIntegrals of TransformsTransform of a Periodic FunctionTransform of the Dirac Delta FunctionFirst Translation Theorem (Translation on the s-axis)Second Translation Theorem (Translation on the t-axis)Convolution Theorem and Its ApplicationsSection 7: Linear Systems of ODEsHomogeneous vs. Nonhomogeneous Linear SystemsComplementary Function, Particular Solution, and General SolutionSuperposition PrincipleHomogeneous Linear Systems with Constant CoefficientsUndetermined CoefficientsVariation of ParametersCONTENT 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 before moving on to the next section.THINGS THAT ARE INCLUDED IN THE COURSE:An instructor who truly cares about your successLifetime access to Ace Ordinary Differential Equations in 17 Hours (The Complete Course)HIGHLIGHTS:#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: Five problem sets at the end of each section (with solutions!) for you to do more practice.#4: Step-by-step guide to help you solve problems.See you inside the course!- Gina:)
