Mathematics · ขั้นสูง · ระดับ 3

Numerical methods

What finite arithmetic does to mathematics: how a number is stored and which values are exact, absolute against relative error, catastrophic cancellation and the rewrites that remove it, and an ill-conditioned problem against an unstable method; root finding by bracketing, fixed-point iteration, Newton and the secant method, with the order each converges at and the hypothesis each order rests on; interpolation by Lagrange and divided differences, its error term, Runge's phenomenon and the splines that answer it; numerical differentiation, the step size that balances truncation against rounding, and the trapezoid, midpoint and Simpson rules with their composite error orders; linear systems by elimination, partial pivoting and LU factorisation, and by Jacobi and Gauss-Seidel iteration; and solvers for initial value problems from Euler through Heun and Runge-Kutta to absolute stability and stiffness.

Ages 18+ 24 lessons about 8 hours in all

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