Taylor Series Expansion

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Example 1 Use Euler method to solve the ODE: dy dx 1 x 2 , y(1) 4 to determine y(1.01), y(1.02) and y(1.03). 26
27 Example 1 0.01 4, 1, , 1 ) , ( 0 0 2 h y x x y x f 9394 3. 1.02 0.011 3.9598 ) , ( 3: 3.9598 1.01 0.011 3.98 ) , ( 2 : 3.98 ) (1) 0.01(1 4 ) , ( 1: ) , ( Method Euler 2 2 2 2 3 2 1 1 1 2 2 0 0 0 1 1 y x f h y y Step y x f h y y Step y x f h y y Step y x f h y y i i i i
Page 1 and 2: The If the Taylor Series Expansion
Page 3 and 4: What If we change the interval ? If
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 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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