Error bounds tell students how accurate an approximation is. This Woody Calculus lesson compares alternating series error with Taylor remainder, explains the first omitted term rule, and shows how Taylor’s theorem controls polynomial approximation error.
Arc length measures the exact distance along a curve by adding infinitely many tiny straight-line distances. This Woody Calculus lesson derives the formula, explains the ds triangle, and solves the classic hard arc length example step by step.
Washer method or shell method? This Woody Calculus lesson teaches the Calculus 2 decision rule for volumes of revolution: identify the function form, check the axis of rotation, choose the right slice, and build the correct volume integral.
Hydrostatic force problems are Calculus 2 slice-method problems in disguise. This Woody Calculus lesson explains why force equals density times gravity times area times depth, why pressure changes with depth, and how to set up the hydrostatic force integral for a circular plate.
Parametric equations describe a point moving through the plane. This Woody Calculus lesson explains how \(x=x(t)\) and \(y=y(t)\) create a directed curve, how to compute \(\frac{dy}{dx}\), and how to find horizontal and vertical tangent lines.
Improper integrals are Calculus 2 limit problems in disguise. This Woody Calculus lesson teaches how to handle infinite intervals, vertical asymptotes, bad points inside an interval, p-integrals, comparison tests, convergence, and divergence with a clear step-by-step system.
Resonance happens when a forcing frequency matches a system’s natural frequency. This Woody Calculus Differential Equations lesson explains forced oscillations, natural frequency, undamped resonance growth, damping, peak response, and real-world applications.
Partial fraction decomposition becomes easier when students stop guessing and identify the denominator type first. This Woody Calculus lesson teaches the complete Calculus 2 system: distinct linear factors, repeated factors, irreducible quadratics, solving for constants, and integrating each piece.
Integration by parts becomes easier when students stop guessing and identify the structure first. This Woody Calculus lesson teaches the complete 3-type IBP system for Calculus 2, including tabular integration by parts, exponential-trig loops, logarithms, inverse trig, and worked examples.
Trig substitution becomes much easier when students stop guessing and match the radical to one of three forms. This Woody Calculus lesson teaches the complete 3-type system for Calculus 2: sine for sqrt(a²−x²), tangent for sqrt(x²+a²), and secant for sqrt(x²−a²).