Newton's Method Explained: Finding Roots with Tangent Lines
How Newton's method finds roots of equations by following tangent lines, the formula, worked examples for √2 and cos x = x, and when it fails.
Calculus
6 guides.
Riemann Sums Explained: Left, Right, Midpoint and Trapezoid
How Riemann sums approximate the area under a curve with rectangles, how left, right, midpoint and trapezoid rules compare, and why they lead to integrals.
Taylor Series Explained: Approximating Functions with Polynomials
What Taylor and Maclaurin series are, how to build them from derivatives, and why sin x ≈ x − x³/6 + x⁵/120 near zero. Clear examples.
Derivatives for Beginners: Power, Product and Chain Rules
Learn what a derivative is and how to differentiate with the power rule, product rule, quotient rule and chain rule, with worked examples.
Integration for Beginners: Antiderivatives and Area
Understand integration as reverse differentiation and as area under a curve. Learn the power rule, definite integrals and integration by parts.
Limits Explained: Substitution, Factoring and L'Hôpital's Rule
What a limit is, how to evaluate one by substitution, factoring or L'Hôpital's rule, and how to handle limits at infinity. Clear worked examples.