Description
For all theoretical assignments, you can turn in as either handwriting or
typing in. For all programming assignments, please turn in your code along
with a solution document. You can discuss questions with others, but the
solutions/codes you submit must be entirely your own work, and please mention
who you collaborated with in your homework.
Software: MATLAB / C++ /Python/Java (or any language that you are
familiar)
Due date: Rutgers time: Mon April 12 2021 23:59 pm
Theoretical assignment Consider the following function
f(x) = exp(x) − exp(-x)
exp(x) + exp(-x)
+ ln(x)
wherex ∈ [1, 5]. Use 5 nodes to uniformly cut the interval [1, 5] into 4 subintervals.
1. Note:
(a) Truncate all numbers to 4 decimal places (5 pts).
(b) Please submit only one single file (Pdf or word), including all the
results (5 pts).
(c) In the solution file,
i. for Q2 and Q3, students can refer Pages 4-5 on the slides-lecture
16.
ii. for Q4, students can refer Page 25 on the slides-lecture 16.
2. Use Trapezoid rule to approximate R 5
1
f(x)dx. (20 pts)
3. Use Simpson’s rule to approximate R 5
1
f(x)dx. (20 pts)
4. Use 2 Gaussian points (n = 1) to evaluate the integration in each subinterval, and sum them up to get the integration over the entire domain.
(50 pts)
1
