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**Newton’s Divided Difference Polynomial Method of Interpolation**

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**Newton’s Divided Difference Method**

Linear interpolation: Given pass a linear interpolant through the data where

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**Figure 2: Velocity vs. time data**

Example The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using the Newton Divided Difference method for linear interpolation. t v(t) s m/s 10 227.04 15 362.78 20 517.35 22.5 602.97 30 901.67 Figure 2: Velocity vs. time data for the rocket example Table 1: Velocity as a function of time

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Linear Interpolation

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**Linear Interpolation (contd)**

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**Quadratic Interpolation**

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**Figure 2: Velocity vs. time data**

Example The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using the Newton Divided Difference method for quadratic interpolation. t v(t) s m/s 10 227.04 15 362.78 20 517.35 22.5 602.97 30 901.67 Figure 2: Velocity vs. time data for the rocket example Table 1: Velocity as a function of time

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**Quadratic Interpolation (contd)**

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**Quadratic Interpolation (contd)**

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**Quadratic Interpolation (contd)**

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General Form where Rewriting

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General Form

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General form

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**Figure 2: Velocity vs. time data**

Example The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using the Newton Divided Difference method for cubic interpolation. t v(t) s m/s 10 227.04 15 362.78 20 517.35 22.5 602.97 30 901.67 Figure 2: Velocity vs. time data for the rocket example Table 1: Velocity as a function of time

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**Example The velocity profile is chosen as**

we need to choose four data points that are closest to

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Example

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Example

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Comparison Table

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Latihan Misalkan Nilai-nilai fungsi seperti pada tabel berikut, tentukanlah nilai aproksimasi dari f(0,1), f(0,35), dan f(1,16) berturut-turut menggunakan interpolasi beda terbagi Newton linear, kuadratik, kubik. x f(x) 0,0 0,000 0,2 0,406 0,4 0,846 0,6 1,368 0,8 2,060 1,0 3,114 1,2 5,114

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**Distance from Velocity Profile**

Find the distance covered by the rocket from t=11s to t=16s ?

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**Acceleration from Velocity Profile**

Find the acceleration of the rocket at t=16s given that

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(x + 4)(x + 7) = x2 + 11x + 28 (x + 14)(x + 2) = x2 + 16x + 28

(x + 4)(x + 7) = x2 + 11x + 28 (x + 14)(x + 2) = x2 + 16x + 28

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