🧮 Calculus I — AristoMind Academy

Master limits, derivatives, integrals, series, and parametric curves — with visual intuition and problem-focused learning.

Calculus I lies at the foundation of physics, engineering, mathematics, data science, and economics. Every chapter includes worked examples, exam-style problems, and a concise exam summary so you know exactly what to learn before a test.

Whether you're preparing for university calculus, already taking it, or reviewing for higher-level math and physics — this book gives you the visual explanations, intuitive derivations, and step-by-step solutions needed to succeed.

📘 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.

🎯 Parametric, Vector & Polar Curves — Parametric derivatives, tangents & normals, polar differentiation, and area in polar coordinates.

📝 Practice & Exam Prep — End-of-chapter problems with solutions and concise exam summaries.

📚 What's Included

✅ 330+ beautifully formatted pages
✅ 200+ fully solved problems
✅ 340+ 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 & Delivery

• 📄 Instant digital PDF access
• 📱 Accessible on phones, tablets, and desktops through your personal login page

🚀 Upgrade your math toolkit today!

Click “Open Sample” to preview the contents, or add to cart to start learning today.