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 seri
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
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 i
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 c
CE 303: Homework #13 (Solution)
Problem #1(a)
y 2 x 3 y
y (1) 2
h 0.1
x 0 1
k1 f x 0 , y 0 2 1 3 2 8
k h
h
k 2 f x 0 , y 0 1 2 1.05 3 2.4 9.3
2
2
y 1.1 y 1 k 2 h 2 0.93 2.93
Problem #1(b)
y xy y
y1
Solution - CE 303: HW#14 Practice Test 3 and Practice Final (50 min or 2 hrs)
Points for each problem are given in parenthesis along the right margin.
Give your final answers in the table whenever pos
UNIVERSITY OF ARIZONA
Department of Civil Engineering & Engineering Mechanics
Guidelines for HOMEWORK Submission
Perhaps the most important thing you will learn as an engineering student is how to sol
Lecture Note of First Few Lectures
1) Function of one variable, its derivative and integral, Function of multiple variables.
1.1) Function of one variable:
In the expression y = f(x), y is known as th
CE 303: Practice Test 1 Solution
Practice Test I - Numerical Analysis and Computer Programming 50
minutes - Closed Lecture Note and HW Solutions
l. Give all possible values of A and B for the followin
CE 303: Homework #8 (Solution)
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
HW#6 Solution
Problem #1
Lagrange Polynomial
3
p ( x ) y i ( x) Li ( x ) y1 L1 ( x) y 2 L2 ( x ) y 3 L3 ( x ) 0 2 L2 ( x ) L3 ( x)
i 1
2
x 0 x 2 x 0 x 1 2 x( x
1 01 2 2 0 2 1
2)
x
( x 1)
2
Newtons
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].
So
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
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 st
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 Polynomia
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 der
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 co
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!
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
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
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 approx
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 win
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 MA
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 t
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 th
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
CE 303: Homework #9_Solution
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 t