All students taking MAT 201 (Numerical Methods) for the Summer 2020 semester are advised to submit the following assignment as part of the regular assignments. All the Assignments are based on lectures 14.
The topics for assignment 1 are as below:

Use Maclaurin series to find approximation of the following functions until approximation error is below 0.1%. If the error is not below 6 terms you can stop a. e^2 b. e^0.5 c. sin 30° d. cos 45°

Use zero through third order Taylor series expansion to predict f(3) using a base point at x=1 f(x)=25x^36x^2+7x88. Compute the true percent relative error for each approximation

Use graphical method to find the root of equation a. Y=5x^3 + 9x^2 + 3x + 2 b. Y=5x^4 + 9x^3 +3x + 2

Use false position and bisection method to find the roots of a. f(x)=0.6x^2+2.4x+5.5 b. f(x)=4x^36x^2+7x2.3 c. f(x)=26 + 85x – 91x^2 + 44x^3 – 8x^4 + x^5 In each case use maximum 6 iteration and break the iteration for error less than 0.1%\

Chapra examples a. 5.1 b. 5.2 c. 5.3 d. 5.4 e. 5.5 f. 5.6

Explain the difference between open and closed method of finding roots.

Use (i) NewtonRaphson (ii) Secant method to find the root of equation a. y=5x^3+9x^2+3x+2 b. y= 5x^4+9x^3+3x+2 c. f(x)= 0.6x^2+2.4x+5.5 d. f(x)= 4x^36x^2+7x2.3 e. f(x)= 26+85x91x^2+44x^38x^4+x^5 In each case use maximum 6 iteration and break the iteration for error less than 0.1%

Explain the difference between Secant method and false position method. Use graphical example to explain the difference.

Implement all the methods shown in this lecture using the language of your choice.

Chapra examples: 6.1  6.6, 6.8
The last date to submit this assignment is August 7, 2020, Friday, 11:59 PM. All the assignments must be handwritten and scanned and sent as PDF files.
The procedure to submit assignments is as follows:
 Prepare your assignment by scanning the handwritten assignments and converting them to PDF. The pages should be in order. I will not make the effort to check misordered files. All the pages should be in a single PDF file.
 Rename your file as MAT201Assignment11901030200XX.pdf, where the last 12 digits are your registration number. Any other format of naming will not be allowed and will not be considered for grading.
 Send your assignment to the following address shparvez@neub.edu.bd. There is no need to CC or send any copy to my other email address.
 The subject line of your email should read as MAT 201 Assignment 1 Summer 2020 by 1901030200XX . Where the last 12 digits are your registration number. Any other format will eliminate the chance of your email to reach the correct folder of my email.