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ASSIGNMENT INSTRUCTIONS

• The deadline will be hardly maintained. No exceptions will be provided without solid proof. So, please start early.
• The assignment has to be handwritten.
• Any plagiarism will directly lead to a zero.
• Assignments will be collected in online form.
• Please rename your assignment file in the following format - “SaadatRafidAhmed_20202020_01” where 01 is representing your section number.
• The assignments will be graded/converted into 15 marks. </aside>

CSE330 Assignment 01

CSE330 Assignment 02

CSE330 Assignment 03

15 Marks Deadline December 5, 2024 11:59 PM (TBA)

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📄 Submission form Q3 📄 ⇒ https://forms.gle/Hb8KfYxCGoRTTD417

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Question 01

Consider the function $f(x) = x \ln(x)$. Now answer the following:

(a) (2 marks) Evaluate the numerical derivative of f(x) at x = 1.0 with step size h = 0.1 using the forward and central difference methods up to 5 significant figures.

(b) ( 2 marks) Compute the upper bound of the truncation error of $f(x)$ at  $x = 1.0$ using $h = 0.1$ for the backward and central difference methods up to 5 significant figures.

(c) (3 marks) Deduce an expression for $D_h^1$ from $D_h$ by replacing $h$ with $(\frac{4h}{3})$ using the Richardson extrapolation method.

(d) (3 marks) For the given $f(x)$ and $x_0 = 1, h = 0.1$, find the error for Richardson extrapolation of degree 1 equation derived in 1(c).

Question 02

1. (3+2 marks) The following Data set is generated by the function $f(x)=x\cos⁡(x)−x+\sin⁡(x)$

Based on the above data, compute $f\prime(1.2)$ using the Central Difference method, and also calculate the relative error. Use 4 significant figures.