Numerical Analysis and Scientific Computing
Explore errors and equation solving; approximation and quadrature; linear systems and differential equations. Concepts and connections are available independently of video coverage.
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Stiff equations
Widely separated decay scales can force explicit methods to take very small stable steps.
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LU factorization
With appropriate pivoting, triangular factors reduce linear-system solution to substitution.
Runge–Kutta methods
Multiple derivative evaluations per step improve ODE approximation accuracy.
Bisection method
Continuity and opposite endpoint signs allow repeated halving to bracket a root.
Conditioning
Conditioning measures sensitivity of a problem's exact solution to perturbations in its data.
Euler method
Euler's method advances an ODE solution using its current derivative and a step size.
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- Runge–Kutta methods · Related · Map context
- LU factorization · Related · Map context