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所在平台: Udemy |
课程主页: https://www.udemy.com/course/basic-differential-equations/
课程评论：没有评论
课程名称：基础微分方程 课程概述：微分方程在物理系统的数学建模中非常重要。许多物理和化学的基本定律可以用微分方程来表述。在生物学和经济学中，微分方程用于建模复杂系统的行为。例如，在经济学中，微分方程用于分析消费者剩余和生产者剩余；在生物学中，则用于分析疾病和病毒（如COVID-19）的传播。微分方程可能是用于开发模型的最常用数学技术，本课程重点教授一阶常微分方程，因为它们是最基本的微分方程形式。本课程还会涉及更高阶的微分方程、拉普拉斯变换、傅里叶方法及偏微分方程等更高级的微分方程方法。 课程有两个基本目的：(1) 帮助学生理解微分方程的概念；(2) 使学生掌握解决一阶微分方程所需的技能。为了在本课程中取得成功，学生至少需要具备扎实的微分和积分计算背景。 课程结束时，学生应能够解决基本的微分方程，并将所学知识应用于各自的学习领域。
Differential equations are very important in the mathematical modeling of physical systems. Many fundamental laws of physics and chemistry can be formulated as differential equations. In biology and economics, differential equations are used to model the behavior of complex systems. For example, in economics, differential equations are used to analyze consumer surplus and producer surplus, and in biology, they are used to analyze the spread of diseases and viruses such as COVID-19.Differential equations are, perhaps, the most utilized mathematical technique to develop models and this course focuses on teaching First-Order Ordinary Differential Equations since they are the most basic form of differential equations to solve. Of course, differential equations do not stop at First-Order. It goes to second and higher orders, it addresses the LaPlace Transformation and the Fourier Method, and Partial Differential Equations; which are all advanced methods in differential equations.This course has two fundamental purposes. (1) to facilitate the comprehension of the student behind the concept of differential equations, (2) to empower students to possess the necessary skills to solve differential equations of first-order. For students to be successful in this course, they must, at least, have a strong background in differential calculus and integral calculus.By the end of this course, students must be able to solve the most basic differential equations and apply what they've learned in their respective fields of study.
