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).
The Frobenius automorphism \(x\mapsto x^p\) is the central symmetry of finite fields. This Woody Calculus Abstract Algebra lesson explains characteristic \(p\), the Freshman’s Dream, cyclic finite-field Galois groups, Frobenius conjugates, trace, norm, unit circles, and how these ideas connect to modern finite-field research.
Why does the simple cubic x³ − 2 create the six-element symmetry group S₃? This Woody Calculus Abstract Algebra lesson explains the roots, splitting field, extension degree, automorphisms, triangle symmetries, and quotient group connection behind one of the cleanest examples in Galois theory.
Learn how to choose the right infinite series test in Calculus 2. This Woody Calculus guide explains the Test for Divergence, p-test, geometric series, Limit Comparison Test, Direct Comparison Test, Ratio Test, Root Test, Integral Test, Alternating Series Test, and telescoping series.
Pointwise convergence checks one input at a time. Uniform convergence controls the whole domain at once. This Woody Calculus Real Analysis lesson explains the definitions, quantifiers, sup norm test, classic examples, and why uniform convergence preserves structure.
Learn how eigenvalues determine phase portraits in Differential Equations. This Woody Calculus lesson explains stable nodes, unstable nodes, saddle points, spiral sinks, spiral sources, centers, repeated eigenvalues, eigenvectors, and stability.
Eigenvalues and eigenvectors reveal the special directions that unlock Linear Algebra and Differential Equations. In this Woody Calculus visual lesson, learn how Av = λv explains matrix transformations, scaling, diagonalization, matrix powers, solution modes, stability, phase portraits, and why eigenvalues predict long-term behavior in systems before you even solve them.
The Riemann Hypothesis is one of the deepest unsolved problems in mathematics. It connects prime numbers, the zeta function, complex analysis, randomness, and hidden order — with a $1,000,000 Clay Mathematics Institute prize for a proof.
After nearly thirty years of teaching advanced mathematics, Brian M. Woody explains how to learn calculus through perfect practice, subconscious training, active recall, sleep science, and identity transformation.