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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Numerical quadrature
Weighted function samples approximate definite integrals with error depending on smoothness and sampling.
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Finite differences
Differences of nearby samples approximate derivatives, balancing truncation and roundoff errors.
Splines
Piecewise polynomials joined with specified smoothness approximate data and curves.
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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- Splines · Related · Map context
- Finite differences · Related · Map context