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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Finite differences
Differences of nearby samples approximate derivatives, balancing truncation and roundoff errors.
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Numerical quadrature
Weighted function samples approximate definite integrals with error depending on smoothness and sampling.
Polynomial interpolation
Distinct nodes determine a unique polynomial of bounded degree passing through their data.
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.
Knowledge connections
- Numerical quadrature · Related · Map context
- Polynomial interpolation · Related · Map context