Single-Variable Calculus

What it means for a function to have a limit, why continuity is the right notion of ‘no sudden jumps’, and h

The derivative as the limit of secant slopes, its interpretation as instantaneous rate of change, and the marginal reaso

The algebra of derivatives - product, quotient and chain rules - plus differentiating relations implicitly a

Approximating a function near a point by a polynomial built from its derivatives - the workhorse behind linearizat

Finding maxima and minima with the first- and second-derivative tests, and applying them to profit maximization and util

The integral as accumulated area, the Fundamental Theorem linking it to antiderivatives, and its use in present value an

When an infinite sum has a finite value, the tests that decide it, and power series - the bridge from geometric di