Numerical Analysis Questions & Answers  
Question by Student 201700278
Dear professor, for the $I_i$ equation discussed in the end of the class today, I think it should be $\frac{\Delta x_i ^{3}}{24}f^{\prime \prime}(x_m)$ instead of $\frac{\Delta x_i ^{3}}{3}f^{\prime \prime}(x_m)$ as you have written in class.
Yes, this is quite possible. You'll need to prove this in the next assignment I think.
Question by Student 201627108
Professor, I have a question about a cubic spline. When we use the cubic spline, Why we assume the only third polynomial like that $$f(x) = ax^{3}+bx^{2}+cx^{1}+d$$ Can we use any different expression such as the exponential function with the natural constant, log function and etc... ?
This may lead to some issues when joining the different polynomials with each other so that the first, second, and third derivatives match. But there may be a way.. Hmm, this is giving me an idea... Maybe I'll ask you a similar question in the final exam..
Question by Student 201529190
Dear professor, when we use the Simpson method every f(xi) need obey 1,4,2,4,2,4,1. There must be odd terms so i think that the problem for the programmer.
You're on the right track but it's not as well explained as it could be. 2 points bonus.
Question by Student 201627131
Professor, I think when we use simpson rule, we must use odd number. Because interval count N-1, and we bound two interval like $$Interval\,I_1 = Between\,i_1,i_2,i_3$$ So, We need even number interval(N-1), and N must odd number.
Yes, very good explanation. 3 points bonus.
Question by Student 201327139
Professor, in Ch.7 assignment Q.3, we have to find

\( \int_{x=0}^{x=2} e^{x^{2}} dx \)

but, your question is ' in the interval \( 1< x < 2 \)'. I'm so confused.
Fixed. Good observation, 2 points bonus.
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