EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 14, Problem 7P
Perform one iteration of the steepest ascent method to locate the maximum of
using initial guesses
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6 108
polynomial is used to approximate v8, the answer is:
dy
13.
of the parametric equations x:
2-3t
3+2t
and y =-
is
dx
Use the following information for Questions 14 and 15:
1+t
1+t
Using the Newton-Raphson method to determine the critical co-ordinate of the graph
y=f(x)=(x)*an (*) (in words x to the power of tan (x)), you will be required to
determine f'(x)
14.
The expression for f'(x) is:
The following tools were required in determining an expression for f'(x):
Application of the natural logarithm
15.
I.
II.
The product rule
III.
Implicit differentiation
For the DE: dy/dx=2x-y y(0)=2 with h=0.2, solve for y using each method below in the range of 0 <= x <= 3:
Q1) Using Matlab to employ the Euler Method (Sect 2.4)
Q2) Using Matlab to employ the Improved Euler Method (Sect 2.5
close all
clear all
% Let's program exact soln
for i=1:5
x_exact(i)=0.5*i-0.5;
y_exact(i)=-x_exact(i)-1+exp(x_exact(i));
end
plot(x_exact,y_exact,'b')
% now for Euler's
h=0.5
x_EM(1)=0;
y_EM(1)=0;
for i=2:5
x_EM(i)=x_EM(i-1)+h;
y_EM(i)=y_EM(i-1)+(h*(x_EM(i-1)+y_EM(i-1)));
end
hold on
plot (x_EM,y_EM,'r')
% Improved Euler's Method
h=0.5
x_IE(1)=0;
y_IE(1)=0;
for i=2:1:5
kA=x_IE(i-1)+y_IE(i-1);
u=y_IE(i-1)+h*kA;
x_IE(i)=x_IE(i-1)+h;
kB=x_IE(i)+u;
k=(kA+kB)/2;
y_IE(i)=y_IE(i-1)+h*k;
end
hold on
plot(x_IE,y_IE,'k')
Q3) Find the optimal solution by using graphical method:.
Max Z = x1 + 2x2
Subject to :
2x1 + x2 < 100
X1 +x2 < 80
X1 < 40
X1, X2 2 0
Chapter 14 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 14 - 14.1 Find the directional derivative of
at in...Ch. 14 - Repeat Example 14.2 for the following function at...Ch. 14 - 14.3 Given
Construct and solve a system of...Ch. 14 - (a) Start with an initial guess of x=1 and y=1 and...Ch. 14 - 14.5 Find the gradient vector and Hessian matrix...Ch. 14 - Prob. 6PCh. 14 - Perform one iteration of the steepest ascent...Ch. 14 - Perform one iteration of the optimal gradient...Ch. 14 - Develop a program using a programming or macro...Ch. 14 - 14.10 The grid search is another brute force...
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