🧮 AP Calculus BC — AristoMind Academy

Master the full AP Calculus BC curriculum — limits, derivatives, integrals, series, and parametric / polar curves — explained visually and reinforced through problem-based learning.

AP Calculus BC is the most advanced high-school calculus course, equivalent to a full year of university calculus. This book helps you truly understand, not cram — through clean visuals, intuitive derivations, and step-by-step examples designed for exam confidence.

Whether you're aiming for a 5️⃣ on the AP exam, preparing for STEM at university, or strengthening math foundations — this is your complete, structured guide.

📘 What You’ll Learn

📈 Functions & Graphs — Domain, range, piecewise functions, transformations, compositions, inverse functions, trig basics.

♾️ Limits & Continuity — Limit laws, one-sided limits, continuity, IVT & EVT, removable vs. non-removable discontinuities.

✏️ Derivatives — Direct computation, product & quotient rule, exponential/log derivatives.

🔗 Chain Rule & Beyond — Chain rule, repeated composition, implicit differentiation, trig & inverse-trig derivatives.

🧭 Graph Analysis with Derivatives — Extrema, asymptotic behavior, graph-sketching, L’Hospital’s Rule.

🧮 Integrals — The integral, FTC, substitution, integration by parts.

🧪 Applications — Area between curves, motion in one dimension (kinematics), volumes of revolution.

🎯 Differential Equations — Modeling, separable DEs, slope fields, qualitative behavior.

🎨 Parametric, Vector & Polar Curves — Parametric derivatives, tangent & normal line, arc length, vector-valued motion, polar differentiation & area, area between two polar curves.

🔁 Series & Convergence — Sequences, convergence tests (limit, ratio, comparison, p-series, Leibniz, integral test), geometric & power series.

🧩 Taylor & Maclaurin Series — Series expansions, differentiation & integration term-by-term, Lagrange error bound.

📝 Exam Prep — End-of-chapter problems, worked solutions, and review summaries.

📚 What's Included

✅ 410+ beautifully formatted pages
✅ 240+ fully solved problems
✅ 200+ original illustrations and diagrams
✅ Exam-focused summaries for each chapter
✅ Clickable boxed equations for instant reference

💡 Why AristoMind?

Written by Daniel Siretanu — Oxford BA + MPhys, PhD researcher in theoretical physics (Queen Mary University of London), former International Physics Olympiad competitor.

“Real understanding comes from solving problems — not memorizing formulas. This course is designed so you can think through calculus — especially under exam pressure.”

📦 Format & Delivery

• Instant digital PDF download
• Works on phones, tablets & desktops

🚀 Your Road to a 5 Starts Here

AP Calculus BC unlocks real mathematical maturity — essential for physics, computer science, engineering, and competitive university admissions.

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👉 Add to Cart to start learning today