Calculus BC

Every lesson in the Calculus BC slide course, in full text: 3 decks, 195 slides.

• The AB Foundations BC Is Standing OnA diagnostic bridge for a student who went straight into BC: limits and indeterminate forms, the derivative as a limit, product and quotient rules, the chain rule, implicit differentiation and related rates, and the Fundamental Theorem with substitution — each traced forward to the BC topic that breaks without it.
• Integration Techniques: Parts, Partial Fractions and Improper IntegralsBC Unit 6 built on its AB foundations: integration by parts as the product rule reversed, partial fractions as common-denominator algebra reversed, improper integrals as the Fundamental Theorem plus a limit, and a thirty-second triage routine for choosing between them.
• Sequences and Infinite Series: Convergence, Geometric Sums and the First TestsThe foundation half of BC Unit 10, built around one distinction: the terms of a series are one sequence, the partial sums are another, and only the partial sums decide. It covers sequences and their limits, the monotone bounded rule, series as limits of partial sums, telescoping and geometric series with their exact totals, the n-th term test and the one-way arrow it lives on, the grouping proof that the harmonic series diverges, and the p-series family used as the reference for every comparison that follows. Every limit, sum and partial sum in the deck was re-derived and checked numerically.