Rolle's theorem - Theorems on Differentiable Functions | Differentiability and Derivatives of Functions - Single-Variable Calculus (Undergraduate Foundation)
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Struggling with a tough concept or looking to advance your skills? Our expert tutors offer one-to-one guidance tailored to your unique needs. Get instant support, clear explanations, and practical strategies to master even the most challenging subjects. With flexible scheduling and customized learning plans, success is just a session away. Book your personalized tutoring today and start achieving your academic goals!
Differentiability and Derivatives of Functions - Single-Variable Calculus (Undergraduate Foundation)Here, you’ll learn what it means for a function to be differentiable and how to compute derivatives using first principles. We explore the derivative as a measure of instantaneous rate of change and as the slope of a tangent line.
The course also highlights the relationship between differentiability and continuity, and includes geometric and physical interpretations of the derivative.
This is where the core machinery of calculus really begins, with the derivative acting as a powerful tool for analysis.
Here, you’ll learn what it means for a function to be differentiable and how to compute derivatives using first principles. We explore the derivative as a measure of instantaneous rate of change and as the slope of a tangent line. The course also highlights the relationship between differentiability and continuity, and includes geometric and physical interpretations of the derivative. This is where the core machinery of calculus really begins, with the derivative acting as a powerful tool for analysis.
![[FUTA, Akure] MTS 102: Introductory Mathematics II](https://media.unidrills.com/avatars/learningTrack/1f_NtYdyMEXxMDcS7AS9.JPEG)
[FUTA, Akure] MTS 102: Introductory Mathematics IIThis learning track is structured for first-year students at the Federal University of technology, Akure (FUTA) and mirrors the standard second-semester coverage of elementary calculus. It begins with single-variable functions and their graphs, then walks learners through limits, continuity, differentiation techniques, and curve sketching—just as covered in the official MTS 102 outline.
You’ll also explore anti-derivatives and integration, learning both the techniques and how to apply them to solve practical problems in science and engineering contexts. Everything is broken down into short, focused video lessons that keep things clear and manageable, especially for students who might be engaging this content for the first time.
If you're not a FUTA student but need to build a solid foundation in these same topics, this track can serve you just as well. The structure and explanations are universal, ensuring that learners with similar academic goals can benefit fully.
This learning track is structured for first-year students at the Federal University of technology, Akure (FUTA) and mirrors the standard second-semester coverage of elementary calculus. It begins with single-variable functions and their graphs, then walks learners through limits, continuity, differentiation techniques, and curve sketching—just as covered in the official MTS 102 outline. You’ll also explore anti-derivatives and integration, learning both the techniques and how to apply them to solve practical problems in science and engineering contexts. Everything is broken down into short, focused video lessons that keep things clear and manageable, especially for students who might be engaging this content for the first time. If you're not a FUTA student but need to build a solid foundation in these same topics, this track can serve you just as well. The structure and explanations are universal, ensuring that learners with similar academic goals can benefit fully.
![[OAU, Ife] MTH 201: Mathematical Methods I](https://media.unidrills.com/LearningTracks/6bnArvzJj3/avatar.JPEG)
[OAU, Ife] MTH 201: Mathematical Methods IComprehensive treatise of advanced calculus covering limits, continuity and differentiability, infinite sequences and series, partial differentiation, numerical methods and ordinary differential equations.
Curated for second-year students of engineering and physical sciences at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.
Comprehensive treatise of advanced calculus covering limits, continuity and differentiability, infinite sequences and series, partial differentiation, numerical methods and ordinary differential equations. Curated for second-year students of engineering and physical sciences at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.
![[UNILAG, Akoka] MTH 102: Elementary Mathematics II](https://media.unidrills.com/avatars/learningTrack/tZoCurnY56fkdaS1QB6e.JPEG)
[UNILAG, Akoka] MTH 102: Elementary Mathematics IIThis learning track is designed to guide first-year students at the University Of Lagos through key concepts in calculus, beginning with the fundamentals of single-variable functions and their graphs. It builds gradually into the core topics of limits, continuity, and differentiability, with each course tailored to simplify these foundational ideas for early learners.
The focus is not just on theory but also on building the skill to solve problems confidently, especially those typically encountered in university-level exams. You’ll move from understanding the concept of a limit to mastering how derivatives work and how to apply them to sketch curves and analyze function behavior.
Although built for UNILAG students, this track is suitable for anyone looking to strengthen their understanding of introductory calculus at the university level. Whether you're preparing for school assessments or seeking a solid refresher, this track will help you follow a structured path.
This learning track is designed to guide first-year students at the University Of Lagos through key concepts in calculus, beginning with the fundamentals of single-variable functions and their graphs. It builds gradually into the core topics of limits, continuity, and differentiability, with each course tailored to simplify these foundational ideas for early learners. The focus is not just on theory but also on building the skill to solve problems confidently, especially those typically encountered in university-level exams. You’ll move from understanding the concept of a limit to mastering how derivatives work and how to apply them to sketch curves and analyze function behavior. Although built for UNILAG students, this track is suitable for anyone looking to strengthen their understanding of introductory calculus at the university level. Whether you're preparing for school assessments or seeking a solid refresher, this track will help you follow a structured path.