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.
Differential Equations & Advanced Applications
Differential Equations & Advanced Applications
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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
- Applied Mathematics
- Mathematics and Mathematical Modeling
- Mathematical Theory & Analysis
- Advanced Mathematics
- Engineering Analysis
- Differential Equations
- Analytical Skills
- Calculus
- Logical Reasoning
- Integral Calculus
- Numerical Analysis
- Mathematical Modeling
- Derivatives
- Engineering Calculations
- 技能部分已折叠。显示 8 项技能，共 14 项。
要了解的详细信息
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8 项作业
February 2026
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该课程共有4个模块
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
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
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
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
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Chaitanya A.
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