CE 303: Homework #9 (Due Date: October 24, 11 pm; Cutoff time: 11 pm, Oct. 25)
Problem 1
20
a) Obtain the 2-point central difference formula for the first derivative of a function from
the Taylor series expansion.
3
b) What is the order of error in the ce
CE 303: Homework #11 (Due Date: 11 pm Nov. 7; Cutoff time: 11 pm, Nov. 8)
1. Solve the differential equation y 2 xy , subjected to the initial condition y 0 2 ,
in domain [0, 1]. Use the following 3 techniques to solve this problem using MATLAB
(a) Use Eu
CE 303: Homework #6 (Due Date: October 3, 11 pm; Cutoff time: 11 pm, Oct. 4)
1. Without using any MATLAB code, obtain by hand calculations the Lagrange polynomial
and Newtons polynomial expressions that will go through the following data points. 10
x
0
1
CE 303: Homework #8 (Due Date: October 17, 11 pm; Cutoff time: 11 pm, Oct. 18)
Problem 1
10
Consider the points
i
1
Xi
0
Yi
2
2
2
4
3
4
5
4
6
8
5
8
16
a) If you use Lagrange polynomials to interpolate these points in the following form
5
p ( x) y i Li ( x
CE 303: Homework #7 (Due Date: October 10, 11 pm; Cutoff time: 11 pm, Oct. 11)
1. Three tensile tests were carried out on an aluminum bar. In each test the strain was
measured at the same values of stress. The results were
Stress (MPa)
Strain (Test 1)
Str
CE 303: Homework #10 (Due Date: 11 pm, October 30; Cutoff time: 1 pm, Oct. 31)
You should not take more than 50 minutes to solve the practice test
1. Consider the following data points
x
y
1
0
2
2
3
3
4
5
5
2
(a) If you want to fit a cubic polynomial of t
CE 303: Homework #12 (Due Date: Nov. 14, 11 pm; Cutoff time: 11 pm, Nov. 15)
1. Consider the differential equation y 2 yy subjected to the initial conditions
y 1 1 and y 1 1 in the interval [1, 5].
Solve the above differential equation by RK2 - midpoint m
CE 303: Homework #13 (Due Date: Nov. 28, 11 pm; Cutoff time: 11 pm, Nov. 29)
1. Do not use any computer code to answer questions (a), (b) and (c).
(a) Consider the differential equation y 2 x 3 y with initial conditions y(1) = 2.
Compute y(1.1) by the sec
CE 303: HW#14 Practice Test 3 and Practice Final (50 min or 2 hrs): For Test 3
solve only the first 2 problems before Nov 30 (1 pm), for final solve all 5 problems.
Points for each problem are given in parenthesis along the right margin.
Give your final a
Homework #4: Solution
Problem 1(a)
my_func1.m
function y=my_func1(x)
y=x+log(x);
Command Window
> x=0.1:0.1:3;
> y=feval('my_func1',x); % you can also write y=my_func(x);
> plot(x,y);hold on; grid on; hold off
Solutions of problems 1(b), (c) and (d) are g
CE 303: Home Work #2_Solution
1.(a) What is the rank of the following matrix?
4
[ A] 1
1
(2 points)
1
4
2
1
2
4
(b) Consider a second matrix [B] as given below.
1
[B ] 4
7
2
2
6
9
3
8
Using MATLAB program check if the following statements are true
CE 303 Numerical Analysis for Civil Engineers
Fall 2016
Catalog Description: (3 units) Finding Roots of Nonlinear Equations, Solution Techniques
for System of Linear Equations, Curve Fitting Polynomial and Spline Interpolation, Least
Squares Fit, Numerica
CE 303: Home Work #1 (Due: 11 pm, Aug. 29, Cutoff time: 11 pm, Aug. 30)
1. Consider the function f ( x) 5 sin x . Note that f(0.25) = 3.535 and f(0.5) = 5.
Knowing the value of f(0.25) and all its derivatives at that point obtain the approximate
value of
CE 303: Homework #5 (Due Date: Sept. 25, 11 pm; Cut-off time: Sept. 26, 1 pm)
Review the materials that you are responsible for in Test 1 and then solve the following practice test problems
without consulting any homework solution or your friends. It is r
HW#3 - Solution
Problem #1
(a) M=15 and N=0. With these values of M and N the determinant of the
coefficient matrix become zero and the ranks of the coefficient matrix [A] and
the augmented matrix [A!b] match; both are equal to 1.
(b) M=15 and N is not eq
CE 303: Home Work #3 (Due Date: 11 pm, Sept. 12, Cutoff time: 11 pm, Sept. 13)
1. Consider the following system of linear equations.
(5 x 2 = 10)
3x + 5y = 0
9x + My = N
(a) What should be the values of M and N for the above system of equations to have
mu
CE 303: Home Work #2 (Due Date: 11 pm, Sept. 5, Cutoff time: 11 pm, Sept. 6)
1.(a) What is the rank of the following matrix?
4
[ A] 1
1
(2 points)
1
4
1
2
4
2
(b) Consider a second matrix [B] as given below.
1
[B ] 4
7
2
2
6
9
3
8
Using MATLAB pro
CE 303: Home Work #1 - Solution
1. Consider the function f ( x) 5 sin x . Note that f(0.25) = 3.535 and f(0.5) = 5.
Knowing the value of f(0.25) and all its derivatives at that point obtain the approximate
value of f(0.5) using the Taylor series expansion
CE 303: Homework #4 (Due: 11 pm, Sept. 19; Cutoff time: 11 noon, Sept. 20)
For the computer programming part of this homework submit the following items:
- Copy of all your commands in the command window
- Any function routine that you have written and us
CE 303: Homework #10 Practice Test Solution
You should not take more than 50 minutes to solve the practice test
1. Consider the following data points
x
y
1
0
2
2
3
3
4
5
5
2
(a) If you want to fit a cubic polynomial of the form y a(x) = ax3 + cx through t