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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Newton's method
A tangent-based iteration approximates a root but convergence depends on the initial point and local hypotheses.
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Bisection method
Continuity and opposite endpoint signs allow repeated halving to bracket a root.
Floating-point arithmetic
Finite-precision arithmetic introduces rounding and has bounded representable ranges.
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.
Finite differences
Differences of nearby samples approximate derivatives, balancing truncation and roundoff errors.
Knowledge connections
- Bisection method · Related · Map context
- Floating-point arithmetic · Related · Map context