🧮 Calculus I — AristoMind Academy
Master the foundations of limits, derivatives, integrals, and series.
This comprehensive Calculus I course is built for first-year students in physics, engineering, and mathematics who want a clear, visual, and problem-focused introduction. It combines strong, rigorous foundations with exam-focused preparation, including dedicated summaries, boxed key formulas, and step-by-step solutions.
📘 What You’ll Learn
📈 Functions & Graphs — Domains, ranges, sketching (including piecewise), compositions, transformations, inverses, trig & hyperbolic basics.
♾️ Limits & Continuity — Properties and techniques for limits, one-sided limits, continuity types, IVT & EVT.
✏️ Derivatives — Linear/polynomial cases, product & quotient rules, exponential/log derivatives.
🔗 Chain Rule & Beyond — Chain rule (incl. repeated composition), higher derivatives, trig/implicit/inverse-trig derivatives.
🧭 Using Derivatives to Understand Graphs — Local/global extrema, asymptotes, and L’Hospital’s rule.
🧮 Integrals: Definitions & Tools — The integral, FTC, indefinite integrals, properties, variable upper bound, substitution, integration by parts.
🧪 Applications of the Integral — Area between curves, kinematics & arc length, solids of revolution, examples from chemistry/physics.
🔁 Series & Convergence — Sequences/series, limit test, absolute/alternating (Leibniz), integral/geometric/p-series, comparison & ratio tests.
🧩 Power, Taylor & Maclaurin Series — Power-series algebra, term-by-term operations, full Taylor/Maclaurin expansions.
📝 Practice & Exam Prep — End-of-chapter problems with solutions and concise exam summaries.
📚 What's Included
✅ 130+ beautifully formatted pages
✅ 45+ fully solved problems
✅ 100+ original illustrations and diagrams
✅ Exam-focused summaries for each chapter
✅ Clickable boxed equations for instant reference
💡 Why AristoMind?
This course was created by someone who’s been through the same journey — trained at Oxford and now pursuing a PhD in theoretical physics at Queen Mary University of London, a leading research institute in the field. His work focuses on scattering amplitudes and their connection to black hole physics. You can learn more on the About Us page and the FAQ page.
"From Physics Olympiad training to my years at Oxford and now deep into PhD research, one lesson has remained constant: real understanding comes from solving problems, not memorizing facts. That’s why this course focuses on clear explanations, step-by-step solutions, and exam-focused summaries — to help you truly grasp and retain the material.
It’s designed for students in physics, engineering, or mathematics who want to build clarity and confidence as they learn."
— Daniel Siretanu, author
📦 Format
Delivered as a high-resolution PDF.
Optimized for phones, tablets, and PCs.
Instant access after purchase.
Upgrade your physics toolkit today.
Click “Open Sample” to preview the contents, or add to cart to start learning today.
