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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.

Øvelser

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

Andre filialer

＋ Arithmetic 𝑥 Algebra △ Geometry ∿ Trigonometry ƒ Precalculus ⊞ Linear Algebra σ Statistics & Probability ⊢ Discrete Math & Logic ℕ Number Theory ẏ Differential Equations ε Analysis ∞ Frontiers