Calculus II – Integrals and Series
A continuation of Calculus I focused on definite integrals, techniques of integration, applications to area and volume, improper integrals, sequences, and series.
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 — 4 lessons
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Integration by partsLesson outline – video coming soon.14m
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Trig integrals & trig substitutionLesson outline – video coming soon.16m
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Partial fractionsLesson outline – video coming soon.16m
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Improper integralsLesson outline – video coming soon.14m
M2
Differentiation — 2 lessons
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Arc length & surface areaLesson outline – video coming soon.14m
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Work & fluid force (examples)Lesson outline – video coming soon.14m
M3
Applications of derivatives — 3 lessons
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Sequences & convergence testsLesson outline – video coming soon.16m
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Series & comparison testsLesson outline – video coming soon.16m
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Alternating & absolute convergenceLesson outline – video coming soon.14m
M4
Integration basics — 2 lessons
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Power series & radius of convergenceLesson outline – video coming soon.16m
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Taylor/Maclaurin seriesLesson outline – video coming soon.16m
M5
Fundamental Theorem of Calculus — 2 lessons
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Parametric curvesLesson outline – video coming soon.12m
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Polar coordinates & area/lengthLesson outline – video coming soon.14m
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.