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18 Cards in this Set
- Front
- Back
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Mean Value Theorem
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f(b) - f(a) / b-a
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Derivative
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f(x+h) - f(x) / h
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Taylors theorem -- around c and for h
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Around c: Sum (k to n) F^k(c) / k! * (x - c)^k
Around h: SUM(k to n) f^k(x) / k ! * h^k |
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How to represent float value
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2^e-127 * 1.m
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Bisection C value
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b - a /2
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Regula Falsi
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b - f(b)(a-b) / f(a) - f(b)
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Newtons
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Xn - f(xn) / f'(xn)
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Secant
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a = xn-1
b = xn b - (b-a) / f(b) - f(a) |
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lagrange
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(x - ..) () / (value - value)() * f0
for all l0s |
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Central Difference
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f(x + h) - f(x - h) / 2h
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Richardson Recursive
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D(N,M) = D(N, M-1) + (1 / 4^m - 1) * (D(N,M-1) - D(N-1, M-1))
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D(0,0)
D(1,0) |
o(h)
o(h/2) |
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trapezoid rule
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(b-a)/2 * [f(a) + f(b)]
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trapezoid error
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-(b-a)/12 * f''(c) * h^2
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composite trapezoid
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(b-a) *[ [f(a) + 2 SUM(f(inner nodes)) + f(b)] / 2n ]
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bisection is good for functions like
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| | | ------------------------------ |
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regula falsi is good for functions like
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\
\ \ \ |
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newton is good for functions
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well behaved with good starting point and calculatable derivative
bad when going circular or flat |
