EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 20, Problem 42P
Repeat Prob.20.41 but determine the coefficients of the polynomial (Sec. 18.4) that fit the data in Table P20.41.
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4. Using the method of Least Squares, determine to 6-decimal place the necessary values of the
coefficient C1 and C2 in the equation from the given data points.
1
y =
C, + C2x
A
C
2.07
8.60
14.42
15.8
Where:
ABCDEF is your student number.
Example, if your student number is 484321.
A = 4
B = 8
C = 4
D = 3
5. Using the same data points given in problem 4, solve for the Newton's Interpolating
Polynomials.
Find the three unknown on this problems using
Elimination Method and Cramer's Rule. Attach your
solutions and indicate your final answer.
Problem 1.
7z 5y
3z
16
%3D
3z
5y + 2z
-8
%3D
5z + 3y
7z
= 0
Problem 2.
4x-2y+3z 1
*+3y-4z -7
3x+ y+2z 5
3. Using the trial function uh(x) = a sin(x) and weighting function wh(x) = b sin(x) find
an approximate solution to the following boundary value problems by determining the value
of coefficient a. For each one, also find the exact solution using Matlab and plot the exact
and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution,
and (iii) plotting the solution)
a.
(U₁xx - 2 = 0
u(0) = 0
u(1) = 0
b. Modify the trial function and find an approximation for the following boundary value
problem. (Hint: you will need to add an extra term to the function to make it satisfy
the boundary conditions.)
(U₁xx - 2 = 0
u(0) = 1
u(1) = 0
Chapter 20 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 20 - 20.1 Perform the same computation as in Sec. 20.1,...Ch. 20 - You perform experiments and determine the...Ch. 20 - 20.3 It is known that the tensile strength of a...Ch. 20 - Prob. 4PCh. 20 - 20.5 The specific volume of a superheated steam is...Ch. 20 - Prob. 6PCh. 20 - In Alzheimers disease, the number of neurons in...Ch. 20 - 20.8 The following data were taken from a stirred...Ch. 20 - Prob. 9PCh. 20 - Concentration data were taken at 15 time points...
Ch. 20 - Prob. 11PCh. 20 - The molecular weight of a polymer can be...Ch. 20 - 20.13 On average, the surface area A of human...Ch. 20 - 20.14 Determine an equation to predict metabolism...Ch. 20 - 20.15 Human blood behaves as a Newtonian fluid...Ch. 20 - 20.16 Soft tissue follows an exponential...Ch. 20 - 20.17 The thickness of the retina changes during...Ch. 20 - 20.18 The data tabulated below were generated from...Ch. 20 - The shear stresses, in kilopascals (kPa), of nine...Ch. 20 - 20.20 A transportation engineering study was...Ch. 20 - The saturation concentration of dissolved oxygen...Ch. 20 - For the data in Table P20.21, use polynomial...Ch. 20 - 20.23 Use multiple linear regression to derive a...Ch. 20 - 20.24 As compared to the models from Probs. 20.22...Ch. 20 - 20.25 In water-resources engineering, the sizing...Ch. 20 - 20.26 The concentration of total phosphorus and...Ch. 20 - 20.27 The vertical stress under the corner of a...Ch. 20 - Three disease-carrying organisms decay...Ch. 20 - 20.29 The mast of a sailboat has a cross-sectional...Ch. 20 - 20.30 Enzymatic reactions are used extensively to...Ch. 20 - 20.31 Environmental engineers dealing with the...Ch. 20 - An environmental engineer has reported the data...Ch. 20 - The following model is frequently used in...Ch. 20 - 20.34 As a member of Engineers Without Borders,...Ch. 20 - 20.35 Perform the same computations as in Sec....Ch. 20 - 20.36 You measure the voltage drop V across a...Ch. 20 - Duplicate the computation for Prob. 20.36, but use...Ch. 20 - The current in a wire is measured with great...Ch. 20 - 20.39 The following data was taken from an...Ch. 20 - It is known that the voltage drop across an...Ch. 20 - Ohms law states that the voltage drop V across an...Ch. 20 - 20.42 Repeat Prob. 20.41 but determine the...Ch. 20 - 20.43 An experiment is performed to determine the...Ch. 20 - Bessel functions often arise in advanced...Ch. 20 - 20.45 The population of a small community on the...Ch. 20 - Based on Table 20.4, use linear and quadratic...Ch. 20 - 20.47 Reproduce Sec. 20.4, but develop an equation...Ch. 20 - 20.48 Dynamic viscosity of water is related to...Ch. 20 - 20.49 Hooke’s law, which holds when a spring is...Ch. 20 - 20.50 Repeat Prob. 20.49 but fit a power curve to...Ch. 20 - The distance required to stop an automobile...Ch. 20 - An experiment is performed to define the...Ch. 20 - The acceleration due to gravity at an altitude y...Ch. 20 - The creep rate is the time rate at which strain...Ch. 20 - 20.55 It is a common practice when examining a...Ch. 20 - The relationship between stress and the shear...Ch. 20 - The velocity u of air flowing past a flat surface...Ch. 20 - 20.58 Andrade’s equation has been proposed as a...Ch. 20 - Develop equations to fit the ideal specific heats...Ch. 20 - 20.60 Temperatures are measured at various points...Ch. 20 - 20.61 The data below were obtained from a creep...
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