Chapter 04.06
Gaussian Elimination More Examples
Civil Engineering
Example 1
To find the maximum stresses in a compound cylinder, the following four simultaneous
linear equations need to be solved.
c1 7.887 10 3
4.2857 10 7 9.2307 10 5
0
0
7
5
7
5.461
Chapter 06.03
Linear Regression-More Examples
Civil Engineering
Example 1
The coefficient of thermal expansion, ,of steel is given at discrete values of temperature in
Table 1.
Table 1 Coefficient of thermal expansion versus temperature for steel.
Tempera
Multiple Choice Test
Chapter 11.04
Discrete Fourier Transform
1.
2.
Given that
(A)
(B)
(C)
(D)
Given that
(A)
(B)
(C)
(D)
W =e
0
1
1
e
W =e
0
1
1
e
2
i
N
2
i
N
, where N = 3 . Then F = W N can be computed as F =
, where N = 3 . F = W
N
2
can be comp
Multiple Choice-Test
Chapter 11.03
Fourier Transform Pair: Frequency and Time
Domain
1.
Given two complex numbers: C1 = 2 3i, and C 2 = 1 + 4i . The product
P = C1 C 2 can be computed as
(A) 2 + 5i
(B) 10 + 5i
(C) 14 + 5i
(D) 14 + 5i
2.
Given the complex
Chapter 03.04
Newton-Raphson Method of Solving a Nonlinear Equation
OBJECTIVES
1.
2.
3.
4.
derive the Newton-Raphson method formula,
develop the algorithm of the Newton-Raphson method,
use the Newton-Raphson method to solve a nonlinear equation, and
discu
Chapter 03.03
Bisection Method of Solving a Nonlinear Equation
After reading this chapter, you should be able to:
1. follow the algorithm of the bisection method of solving a nonlinear equation,
2. use the bisection method to solve examples of finding roo
Chapter 04.07
LU Decomposition More Examples
Civil Engineering
Example 1
To find the maximum stresses in a compound cylinder, the following four simultaneous
linear equations need to solved.
c1 7.887 10 3
4.2857 10 7 9.2307 10 5
0
0
7
5
7
5.4619 10 5
Multiple Choice Test
Chapter 11.05
Informal Development of Fast Fourier Transform
Using the definition W = e
1.
i
2
N
, and the Euler identity e i = cos( ) i sin( ) , the
N
value of W 6 can be computed as
(A) 0.866 0.5i
(B) 0.866 + 0.5i
(C) 0.5 0.866i
(D)
Chapter 03.03
Bisection Method of Solving a Nonlinear Equation
OBJECTIVES
1. follow the algorithm of the bisection method of solving a nonlinear equation,
2. use the bisection method to solve examples of finding roots of a nonlinear equation, and
3. enume
Chapter 08.02
Eulers Method for Ordinary Differential EquationsMore Examples
Civil Engineering
Example 1
A polluted lake has an initial concentration of a bacteria of 10 7 parts/m 3 , while the
acceptable level is only 5 10 6 parts/m 3 . The concentration
Multiple-Choice Test
Chapter 08.06
Shooting Method
1.
The exact solution to the boundary value problem
d2y
= 6 x 0.5 x 2 , y (0) = 0 , y (12 ) = 0
2
dx
for y (4 ) is
(A) -234.66
(B) 0.00
(C) 16.000
(D) 106.66
2.
Given
d2y
= 6 x 0.5 x 2 , y (0) = 0 , y (12
Chapter 03.01 Solution of Quadratic Equations
After reading this chapter, you should be able to: 1. find the solutions of quadratic equations, 2. derive the formula for the solution of quadratic equations, 3. solve simple physical problems involving quadr
Chapter 07.03
Simpsons 1/3 rd Rule
OBJECTIVES
1.
2.
3.
4.
5.
derive the formula for Simpsons 1/3 rule of integration,
use Simpsons 1/3 rule it to solve integrals,
develop the formula for multiple-segment Simpsons 1/3 rule of integration,
use multiple-segm
Chapter 08.03
Runge-Kutta 2nd Order Method for
Differential Equations-More Examples
Civil Engineering
Ordinary
Example 1
A polluted lake has an initial concentration of a bacteria of 10 7 parts/m 3 , while the
acceptable level is only 5 10 6 parts/m 3 . T
Multiple-Choice Test
Chapter 08.06
Shooting Method
1.
The exact solution to the boundary value problem
d2y
= 6 x 0.5 x 2 , y (0) = 0 , y (12 ) = 0
2
dx
for y (4 ) is
(A) -234.66
(B) 0.00
(C) 16.000
(D) 106.66
2.
Given
d2y
= 6 x 0.5 x 2 , y (0) = 0 , y (12
Chapter 07.02
Trapezoidal Rule
OBJECTIVES
1.
2.
3.
4.
5.
derive the trapezoidal rule of integration,
use the trapezoidal rule of integration to solve problems,
derive the multiple-segment trapezoidal rule of integration,
use the multiple-segment trapezoid
Chapter 08.04
Runge-Kutta 4th Order Method for
Differential Equations-More Examples
Civil Engineering
Ordinary
Example 1
A polluted lake has an initial concentration of a bacteria of 10 7 parts/m 3 , while the
acceptable level is only 5 10 6 parts/m 3 . T
Multiple Choice Test
Chapter 11.02
Continuous Fourier Series
1.
Which of the following is an even function of t ?
(A) t 2
(B) t 2 4t
(C) sin( 2t ) + 3t
(D) t 3 + 6
2.
A periodic function is given by a function which
(A) has a period T = 2
(B) satisfies f
Chapter 03.01
Solution of Quadratic Equations
OBJECTIVES
1. find the solutions of quadratic equations,
2. derive the formula for the solution of quadratic equations,
3. solve simple physical problems involving quadratic equations.
Chapter 03.04
Newton-Raphson Method of Solving a Nonlinear
Equation
After reading this chapter, you should be able to:
1.
2.
3.
4.
derive the Newton-Raphson method formula,
develop the algorithm of the Newton-Raphson method,
use the Newton-Raphson method
Chapter 05.02
Direct Method of Interpolation More Examples
Computer Engineering
Example 1
A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a
15"10" rectangular plate. The centers of the holes in the plate describe
MULTIPLE CHOICE TEST: GAUSS-SEIDEL METHOD: SIMULTANSOUS LINEAR EQUATIONS
Multiple-Choice Test
Gauss-Seidel Method of Solving
Simultaneous Linear Equations
1. A square matrix [A]nxn is diagonally dominant if
n
(A) aii aij , i = 1, 2, , n
j 1
i j
n
n
j 1
i
Chapter 08.05
On Solving Higher Order Equations for Ordinary Differential Equations
OBJECTIVES
1. solve higher order and coupled differential equations
Chapter 05.04
Lagrange Method of Interpolation More Examples
Computer Engineering
Example 1
A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a
15"10" rectangular plate. The centers of the holes in the plate describ