APM4813/101/0/2022 8.4 Assignments Assignment 01 Recommended closing date: 03 May 2022 Question 1: The Bisection method:

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Apm4813 101 0 2022 8 4 Assignments Assignment 01 Recommended Closing Date 03 May 2022 Question 1 The Bisection Method 1 (29.33 KiB) Viewed 13 times

Apm4813 101 0 2022 8 4 Assignments Assignment 01 Recommended Closing Date 03 May 2022 Question 1 The Bisection Method 2 (26.78 KiB) Viewed 13 times

Apm4813 101 0 2022 8 4 Assignments Assignment 01 Recommended Closing Date 03 May 2022 Question 1 The Bisection Method 3 (20.54 KiB) Viewed 13 times

APM4813/101/0/2022 8.4 Assignments Assignment 01 Recommended closing date: 03 May 2022 Question 1: The Bisection method: Consider the function () = 3x + sin(x) - (1.1) Use the basection method to determine a root of $(x) in the Interval (0,0,0.5), using up to ten iterations (10) (1.2) Repeat the above question by using Mathematica commands. Give a command to generate each iteration. Present all commands and results generated. (10) (1.3) Give a single Mathematica command that determines a root of f(a) in the interval (0.0.0.5), and run it. Present all the results. (1:4) Give a single Mathematica command that plots (*) in the interval 0.0 <<0.5 and 0 <f(x) < 2, label the nxes accordingly as I and f(x). Present both the cotumand and the plot. (2) [25 Question 2: Newton's method: Consider the same function (*) - 3x + sin(x)- (2.1) Use the Newton's method method to determine a root of f(x) in the interval (0,0,0.5), tusing up to ten iterations (10)

(2.2) Repeat the above question by using Mathematica commands. Give a command to generate each iteration, tising Newton's method. Present all commands and results generated (10) (2:3) Give a single Mathematics command that plots }(x) = x2 +212-1+5 in the interval 0.0<=< 0.5 and 0 <f(x) < 5, label the axes accordingly as I and f(x). Determine the root graphically, by estimating it off the plot. Present both the command and the plot. (5) (25) Question 3: The r = 9(1) method: Use the r = 9(r) method to determine the root of f(a) mentioned in Question 1. Provide the same details asked for (25) Question 4: Lagrangian interpolation: Suppose that we have the following data paine-s-values and S(+)-values where f(x) is some unknown function: Table 0.0.1: Data for curve fitting (2) 3.2 25.4 2.7 20.6 1.0 16.2 4.8 413 5.6 59.8 (4.1) Use the Lagrangian polynomial to interpolate the data in the table.

7 APM4813/101/0/2022 (4.2) Repeat the above question by using Mathematica commands. Give a command to generate the whole interpolation. Present all commands and results generated. (5) (4.3) Give a single Mathematica command that uses Lagrangian polynomial to interpolate the data in the table. (5) (4.4) Plot the points in the table using mathematica, (5) (4.5) Plot the interpolation polynomial you obtained using mathematica. (5) [25] TOTAL: (100)