Taylor Series Expansion

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Maclaurin Series Maclaurin series is a special case of Taylor series with the center of expansion c = 0. The f If (0) the Maclaurin series (2) ' f (0) f (0) x 2! series converge, expansion of (3) ( x) : 2 f (0) 3 x x ... 3! we can write : f f ( x) ∞ ∑ k0 1 k! f ( k) (0) x k
What If we change the interval ? If we change the interval so x=x+h and c=x The Taylor series expansion of f ( x h) about c x f ( x h) f ( x) f ' ( x) h f ( x) 2! (2) h 2 f ( x) 3! (3) h 3 ...
Page 1: The If the Taylor Series Expansion
Page 5 and 6: Finite Differences for Derivation T
Page 7 and 8: Example : Derivation of Forward Dif
Page 9 and 10: Example : Derivation of Forward Dif
Page 11 and 12: Derivatives of Bivariate & Multivar
Page 13 and 14: Second Partial Derivatives hk k y h
Page 15: Second Partial Derivatives Followin
Page 18 and 19: Taylor Series Method The problem to
Page 20 and 21: Euler Method • First order Taylor
Page 22 and 23: 22 Euler Method 1,2,... ) , ( ) ( M
Page 24 and 25: Interpretation of Euler Method y 1
Page 26 and 27: Example 1 Use Euler method to solve
Page 28 and 29: Example 1 f 2 ( x, y) 1 x , x0 1, y
Page 30 and 31: Example 1 f 2 ( x, y) 1 x , x0 1, y
Page 32 and 33: Second Order Taylor Series Methods
Page 34 and 35: 34 High Order Taylor Series Methods
Page 36 and 37: Example 2 Second order Taylor Serie
Page 38 and 39: 38 Example 2 )) 2 (1 4 1 ( 2 ) 2 (1
Page 40 and 41: Programming Euler Method Write a MA
Page 42 and 43: Programming Euler Method f=inline('
Page 44 and 45: Example 1: Find y(0.5) if y is the
Page 46 and 47: Example 3: Solve the differential e
Page 48: Comparison of numerical and analyti

Taylor Series Expansion

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