Review1

Review1 - f x i Δ x = f x i Δ x f ± x i Δ x 2 2 f ± x...

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Test I Review MAT 421 Applied Computational Methods Numerical Diferentiation (memorize Formulas For f ± f ± ) (2) Lagrange Interpolation (memorize) (3) Numerical Integration (memorize TR, Richardson extrapolation) Initial Value Problems memorize Forward Euler, backward Euler, TR understand RK2, RK4 (4) accuracy (LTE), (5) stability ( | G |≤ 1), convergence Equivalence Theorem Memorize Taylor Series Expansion:
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Unformatted text preview: f ( x i +Δ x ) = f ( x i )+Δ x f ± ( x i )+ Δ x 2 2! f ± ( x i )+ Δ x 3 3! f (3) ( x i )+ Δ x 4 4! f (4) ( x i )+ · · · f ( x i-Δ x ) = f ( x i )-Δ x f ± ( x i )+ Δ x 2 2! f ± ( x i )-Δ x 3 3! f (3) ( x i )+ Δ x 4 4! f (4) ( x i )-··· Redundant truth doesn’t bother us! –Feynman u ( t n + Δ t ) = u ( t n ) + Δ t u ± ( t n ) + Δ t 2 2! u ± ( t n ) + Δ t 3 3! u (3) ( t n ) + Δ t 4 4! u (4) ( t n ) + · · ·...
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