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Calculus 2

Techniques of integration, differential equations, series, and parametric and polar curves. 257 problems, in the order most textbooks teach them.

Techniques of integration

Undo the product rule: ∫u dv = uv − ∫v du.

Powers and products of sines and cosines, with identities.

Split a rational function into simple pieces, then integrate each.

Infinite intervals and infinite integrands: replace the bad bound with a limit.

Separate the variables, integrate both sides, and use the initial condition.

The integrating factor method for y′ + p(x)y = q(x).

Σ arⁿ converges to a/(1 − r) exactly when |r| < 1.

Divergence, p-series, integral, comparison and ratio tests: which one, and why.

Where a power series converges, found with the ratio test.

Polynomial approximations built from derivatives at a point.

dy/dx = (dy/dt)/(dx/dt), and the tangent line at a parameter value.

½∫ r² dθ: petals, cardioids and circles.