maths.free › Analysis
Analysis
Analysis is calculus with the reasons attached: what a limit really is, when a series converges and why, what makes a function continuous or differentiable, and how the same ideas extend to the complex plane. It is the language the open problems are written in.
_Öyrən
Core
Sequences and their limits
What it means for aₙ to approach L, and the limits that define e and π.
limit of (1 + 1/n)^n as n -> oo
Core
Convergence of series
Divergence, ratio, comparison and integral tests — and the harmonic series.
does 1/n^2 for n = 1 to oo converge
Core
Improper integrals
Integrals to infinity or across a singularity, defined as limits.
integrate 1/x^2 dx from 1 to oo
Advanced
Taylor approximation and error
How well a polynomial stands in for a function, and how far you can trust it.
taylor series of sin(x)
Advanced
Functions of a complex variable
Euler's formula, and why complex analysis is where the Riemann Hypothesis lives.
e^(i*pi)
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