Differential Equations & Advanced Applications

位教师：Stavros Richard Christopoulos

包含在中

了解更多

4个模块

深入了解一个主题并学习基础知识。

中级等级

推荐体验

1 周完成

在 10 小时一周

灵活的计划

自行安排学习进度

为学位做准备

了解更多

4个模块

深入了解一个主题并学习基础知识。

中级等级

推荐体验

1 周完成

在 10 小时一周

灵活的计划

自行安排学习进度

为学位做准备

了解更多

您将学到什么

Apply product, quotient, and chain rules to solve real-world rate-of-change problems in science and business.
Use derivatives for optimization, identifying maxima, minima, and inflection points in practical applications.
Perform implicit and higher-order differentiation to model interdependent variables and dynamic systems.
Apply derivatives to gradient estimation, curve analysis, and optimization in data science and engineering.

您将获得的技能

要了解的详细信息

可分享的证书

添加到您的领英档案

了解顶级公司的员工如何掌握热门技能

了解关于 Coursera for Business 的更多信息

Petrobras, TATA, Danone, Capgemini, P&G 和 L'Oreal 的徽标

该课程共有4个模块

Master the foundational principles of differential calculus and unlock analytical capabilities essential for data science, engineering, and advanced mathematics. This course provides comprehensive training in derivative calculations, optimization techniques, and real-world problem-solving applications. Through systematic exploration of differentiation rules, implicit differentiation, and critical point analysis, you will develop robust mathematical reasoning skills applicable across scientific and business domains. Learn to model dynamic systems, analyze rates of change, and apply calculus techniques to solve complex optimization challenges. Whether advancing in quantitative fields or building analytical foundations for graduate studies, this course equips you with rigorous mathematical frameworks and practical computational skills to excel in data-driven decision-making and technical problem-solving.

This week you will begin solving first-order linear ordinary differential equations using integrating factors. You can also explore how these equations model real-world systems and practice solving them step by step.

涵盖的内容

2个视频7篇阅读材料2个作业

2个视频总计4分钟

Welcome2分钟
Instructions for the week3分钟

7篇阅读材料总计70分钟

What to expect from this course10分钟
Overview10分钟
Self-Study on the Definition of ODEs10分钟
Self-Study on First-Order Linear ODEs10分钟
Step-by-Step Examples of First order ODEs - Questions10分钟
Step-by-Step Examples of First order ODEs - Solutions10分钟
Summary10分钟

2个作业总计60分钟

Let's Practice: First-Order Linear Ordinary Differential Equations30分钟
Test Yourself: First-Order Linear Ordinary Differential Equations30分钟

This week introduces you to second-order linear ODEs with constant coefficients. You will learn to solve them using characteristic equations and apply your understanding to model dynamic systems.

涵盖的内容

2个视频6篇阅读材料2个作业

2个视频总计4分钟

Welcome1分钟
Instructions for the week3分钟

6篇阅读材料总计60分钟

Overview10分钟
Self-Study on Second-Order Linear ODEs10分钟
Second-Order Equations with Constant Coefficients10分钟
Examples of Second-Order Linear ODEs - Questions10分钟
Examples of Second-Order Linear ODEs - Solutions10分钟
Summary10分钟

2个作业总计60分钟

Let's Practice: Second-Order Linear Ordinary Differential Equations30分钟
Test Yourself: Second-Order Linear Ordinary Differential Equations30分钟

This week you will continue to explore second-order ODEs by applying initial and boundary conditions to find unique solutions. You will also explore integrating factors and real-world applications such as mechanical and electrical systems.

涵盖的内容

2个视频10篇阅读材料2个作业

2个视频总计5分钟

Welcome1分钟
Instructions for the week4分钟

10篇阅读材料总计100分钟

Overview10分钟
Self-Study on Initial and Boundary Conditions for Second-Order ODEs10分钟
Worked Examples on Applying Conditions to ODEs - Questions10分钟
Worked Examples on Applying Conditions to ODEs - Solutions10分钟
Worked Examples Using Integrating Factors - Questions10分钟
Worked Examples Using Integrating Factors - Solutions10分钟
Study of Practical Examples Involving Applications10分钟
Examples of Second-Order ODEs with Initial/Boundary Conditions and Integrating Factors - Questions10分钟
Examples of Second-Order ODEs with Initial/Boundary Conditions and Integrating Factors - Solutions10分钟
Summary10分钟

2个作业总计60分钟

Let's Practice: Second-Order Linear Ordinary Differential Equations (Continuation)30分钟
Test Yourself: Second-Order Linear Ordinary Differential Equations (Continuation)30分钟

The focus in this module is moving to partial differentiation, where you will learn to compute partial derivatives for multivariable functions. You can then practice interpreting these derivatives in context and apply them to data modelling.

涵盖的内容

2个视频7篇阅读材料2个作业1个插件

2个视频总计4分钟

Welcome1分钟
Instructions for the week2分钟

7篇阅读材料总计70分钟

Overview10分钟
Self-Study on Partial Differentiation Concepts10分钟
Worked Examples of Partial Differentiation - Questions10分钟
Worked Examples of Partial Differentiation - Solutions10分钟
Examples of Partial Differentiation - Questions10分钟
Examples of Partial Differentiation - Solutions10分钟
Summary of the course and next steps 10分钟

2个作业总计60分钟

Let's Practice: Partial Differentiation30分钟
Test Yourself: Partial Differentiation30分钟

1个插件总计15分钟

Attempt-and-Check Solved Examples15分钟

为学位做准备

学习 University of Huddersfield 的这个课程，您可以预览相关学位课程计划中的主题、材料和授课教师，以便您确定该主题或大学是否适合您。

位教师

Stavros Richard Christopoulos

University of Huddersfield

3 门课程362 名学生

提供方

University of Huddersfield

从 Math and Logic 浏览更多内容

University of Huddersfield
Differential Calculus Fundamentals
课程
状态：免费试用
The Hong Kong University of Science and Technology
Differential Equations for Engineers
课程
状态：预览
Korea Advanced Institute of Science and Technology(KAIST)
Differential Equations Part III Systems of Equations
课程
状态：预览
Korea Advanced Institute of Science and Technology(KAIST)
Differential Equations Part II Series Solutions
课程

人们为什么选择 Coursera 来帮助自己实现职业发展

Felipe M.

自 2018开始学习的学生

''能够按照自己的速度和节奏学习课程是一次很棒的经历。只要符合自己的时间表和心情，我就可以学习。'

Jennifer J.

自 2020开始学习的学生

''我直接将从课程中学到的概念和技能应用到一个令人兴奋的新工作项目中。'

Larry W.

自 2021开始学习的学生

''如果我的大学不提供我需要的主题课程，Coursera 便是最好的去处之一。'

Chaitanya A.

''学习不仅仅是在工作中做的更好：它远不止于此。Coursera 让我无限制地学习。'

通过 Coursera Plus 开启新生涯

无限制访问 10,000+ 世界一流的课程、实践项目和就业就绪证书课程 - 所有这些都包含在您的订阅中

了解更多

通过在线学位推动您的职业生涯

获取世界一流大学的学位 - 100% 在线

探索学位

加入超过 3400 家选择 Coursera for Business 的全球公司

提升员工的技能，使其在数字经济中脱颖而出

了解更多

常见问题

To access the course materials, assignments and to earn a Certificate, you will need to purchase the Certificate experience when you enroll in a course. You can try a Free Trial instead, or apply for Financial Aid. The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.

When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile.

Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.