Technological Institute of the Philippines
Math 011 - Advanced Engineering Mathematics
Engr. Cedie B. Macalisang
Homework 2.2
Numerical Differentiation and Integration
๏ท Numerical Differentiation
Approximate for the definite differentials of the functions below @ x = ฯ. Compare FDM, BDM, and CDM
results with analytical method.
1. ๐(๐ฅ)= ๐ฅ4โ ๐ฅ3+ 1
2. ๐(๐ฅ)= cos(๐ฅ)+ln (๐ฅ)
๏ท Numerical Integration
Use both (a)Trapezoidal and (b)1/3 Simpson's Rules to solve for the definite integrals below. Also, (c)
provide the corresponding graphs as accurate as possible. Tabulate the functions of x's if you must.
(d) Using error tests, which method is better fit for each function? (e) If you wish to achieve ๐ธ = 0.0001,
how many intervals for each method must be made?
3. ๐(๐ฅ)= ๐ฅ4โ ๐ฅ3+ 1; from 0 to 1.5 with n = 10
4. ๐(๐ฅ)= cos(๐ฅ)+ln (๐ฅ); from 0.5 to 3.5 n = 10
