Aproximarea functionalelor liniare

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$P 0.1 Stabilişti natura şsi suma seriilor: a) Σ 1 n\ ; b) Σ arctan 1 n# + n ...$

Introducere Derivare numerică Integrare numerică Cuadraturi adaptive Cuadraturi . . . Cuadraturi . . . Formule . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 24 of 58 Go Back Full Screen Close Quit Această formulă se nume¸ste regula (elementară a) trapezului. Însumând pentru toate subintervalele se obt¸ine regula trapezelor sau formula compusă a trapezului sau formula repetată a trapezului. b a 1 f(x)dx = h 2 f0 + f1 + · · · + fn−1 + 1 2 fn − 1 12 h3 n−1 f ′′ (ξk). Deoarece f ′′ este continuă pe [a, b], restul se poate scrie sub forma k=0
Introducere Derivare numerică Integrare numerică Cuadraturi adaptive Cuadraturi . . . Cuadraturi . . . Formule . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 24 of 58 Go Back Full Screen Close Quit Această formulă se nume¸ste regula (elementară a) trapezului. Însumând pentru toate subintervalele se obt¸ine regula trapezelor sau formula compusă a trapezului sau formula repetată a trapezului. b a 1 f(x)dx = h 2 f0 + f1 + · · · + fn−1 + 1 2 fn − 1 12 h3 n−1 f ′′ (ξk). Deoarece f ′′ este continuă pe [a, b], restul se poate scrie sub forma (b − a)h2 R1,n(f) = − f 12 ′′ (b − a)3 (ξ) = − 12n2 f ′′ (ξ). (21) k=0
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Aproximarea functionalelor liniare

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