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
Access provided by PALC Dev
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
- Engineering Calculations
- Advanced Mathematics
- Integral Calculus
- Applied Mathematics
- Calculus
- Logical Reasoning
- Derivatives
- Numerical Analysis
- Engineering Analysis
- Mathematical Modeling
- Mathematical Theory & Analysis
- Differential Equations
- Analytical Skills
- Mathematics and Mathematical Modeling
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Details to know
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8 assignments
February 2026
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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
Prepare for a degree
Taking this course by University of Huddersfield may provide you with a preview of the topics, materials and instructors in a related degree program which can help you decide if the topic or university is right for you.
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