Calculus 1,
Rebuilt From Zero

Domains, function families, composition, transformations, the unit circle in radians, exponent and log rules, and the factoring skills that resolve 0/0 limits.

Approaching vs. arriving, one-sided limits, defeating 0/0 with factoring and conjugates, the Squeeze Theorem, asymptotes, and the two special trig limits.

The three-part definition, removable vs. jump vs. infinite discontinuities, gluing piecewise functions, and the Intermediate Value Theorem.

Secant to tangent, the limit definition and its alternate form, notation, interpretation with units, tangent lines, and where differentiability fails.

Power, product, quotient, and chain rules — the four moves that replace limit computations with algebra, plus the rewrite-first habit that prevents most errors.

Trig, exponentials, logarithms, and inverse trig — the formula card to memorize cold, every chain-rule variant, and logarithmic differentiation.

Differentiating curves not solved for y, tangents to circles and folia, and the five-step related-rates method: ladders, cones, shadows, and departing cars.

Critical points, both derivative tests, concavity and inflection, absolute extrema on closed intervals, the Mean Value Theorem, and curve sketching.

The six-step translation from word problem to one-variable max/min hunt — fences, boxes, cans, closest points, revenue, and the swimmer who discovers Snell's law.

Reversing the derivative, Riemann sums, the definite integral, both parts of the Fundamental Theorem of Calculus, and u-substitution — the bridge to Calc 2.