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
Instructor: Stavros Richard Christopoulos
Included with
Recommended experience
What you'll learn
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.
Skills you'll gain
- Logical Reasoning
- Numerical Analysis
- Engineering Analysis
- Differential Equations
- Advanced Mathematics
- Mathematical Modeling
- Mathematics and Mathematical Modeling
- Mathematical Theory & Analysis
- Derivatives
- Applied Mathematics
- Engineering Calculations
- Analytical Skills
- Calculus
- Integral Calculus
- Skills section collapsed. Showing 7 of 14 skills.
Details to know
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February 2026
8 assignments
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There are 4 modules in this course
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.
What's included
2 videos7 readings2 assignments
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.
What's included
2 videos6 readings2 assignments
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.
What's included
2 videos10 readings2 assignments
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.
What's included
2 videos7 readings2 assignments1 plugin
Instructor
Offered by
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University of Huddersfield
Status: Free TrialThe Hong Kong University of Science and Technology
Status: PreviewKorea Advanced Institute of Science and Technology(KAIST)
Status: PreviewKorea Advanced Institute of Science and Technology(KAIST)
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Frequently asked questions
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.
More questions
Financial aid available,