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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.
Lessons
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
Other branches
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