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Calculus

The mathematics of change. Derivatives here are taken one rule at a time (power, product, chain…), integrals show the technique they use (substitution, parts, partial fractions), and every result is graphed against the original.

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Introductory Limits Substitution, factoring and L'Hôpital's rule. limit of sin(x)/x as x -> 0 Core Derivatives Power, product, quotient and chain rules, applied one at a time. derivative of sin(x)*x^2 Core Integrals Antiderivatives by substitution, parts and partial fractions. integral of x*e^x dx Core Definite integrals Area under a curve and the fundamental theorem of calculus. integrate x^2 dx from 0 to 1 Advanced Taylor series Approximating a function by polynomials built from its derivatives. taylor series of e^x Advanced Series and sums Partial sums, closed forms and convergence. sum of 1/n^2 for n = 1 to oo Core Maxima and minima Critical points and the second-derivative test. critical points of x^3 - 3x

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