Calculus I – Limits and Derivatives
A first university level calculus course covering functions, limits, continuity, derivatives, and core applications such as rates of change and optimization.
What you’ll learn
- Turn word problems into clear mathematical models
- Use the right theorem or method without guessing
- Blend analytic techniques with numerical intuition
- Check your own work with simple sanity checks and visuals
Curriculum
M1
Limits & continuity — 2 lessons
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Limits from graphs & algebraLesson outline – video coming soon.14m
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Continuity & intermediate valueLesson outline – video coming soon.12m
M2
Differentiation — 3 lessons
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Definition of derivativeLesson outline – video coming soon.12m
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Rules (product/quotient/chain)Lesson outline – video coming soon.16m
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Implicit differentiationLesson outline – video coming soon.12m
M3
Applications of derivatives — 2 lessons
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Optimization & related ratesLesson outline – video coming soon.16m
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Mean value theorem & monotonicityLesson outline – video coming soon.14m
M4
Integration basics — 4 lessons
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Antiderivatives & substitutionLesson outline – video coming soon.16m
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Area & Riemann sumsLesson outline – video coming soon.12m
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FTC I & IILesson outline – video coming soon.14m
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Average value & applicationsLesson outline – video coming soon.12m
Projects
- Model a real-world system (growth, decay, motion, or heat flow) or dataset
- Write a short report comparing analytic and numerical solutions
- Create study notes and formula sheets you can reuse in exams
Prerequisites
- Prior exposure to high-school algebra and functions
- For ODE/PDE: at least Calculus I (or concurrent)
- Willingness to pause and re-watch explanations until they click
Who is this for?
- Students currently in a university math course who want a second pass
- STEM majors building a stronger analysis foundation
- Self-taught learners filling in gaps before ML/AI or physics
Outcomes
- Less “formula hunting”, more structured problem-solving
- A reusable set of notes, diagrams, and checklists
- More confidence walking into problem sets and exams
Resources
- Starter project / template (ZIP)
- Setup & study checklists (PDF)
- Core formulas / syntax cheatsheet (PDF)
Tip: Right-click → “Save link as…” if your browser opens the file.
FAQ
Is this beginner-friendly?
Yes. We start from mental models and build up with guided practice and plenty of worked examples.
Will I need extra software?
We stick to free or standard tools. Any optional extras are clearly marked and have alternatives.
Do I get updates?
Yes—lifetime access with updates as the field, tools, and exam expectations evolve.