EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 17, Problem 30P
Derive the least-squares fit of the following model:
That is, determine the coefficients that results in the least-squares fit for a second-order polynomial with a zero intercept. Test the approach by using it to fit the data from Prob. 17.28.
Expert Solution & Answer
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Students have asked these similar questions
3. Using the trial function u¹(x) = a sin(x) and weighting function w¹(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
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
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.
Chapter 17 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 17 - Given these data 8.8 9.5 9.8 9.4 10.0 9.4 10.1 9.2...Ch. 17 - Given these data 29.65 28.55 28.65 30.15 29.35...Ch. 17 - 17.3 Use least-squares regression to fit a...Ch. 17 - 17.4 Use least-squares regression to fit a...Ch. 17 - 17.5 Using the same approach as was employed to...Ch. 17 - Use least-squares regression to fit a straight...Ch. 17 - Fit the following data with (a) A...Ch. 17 - Fit the following data with the power model...Ch. 17 - 17.9 Fit an exponential model...Ch. 17 - 17.10 Rather than using the base-e exponential...
Ch. 17 - 17.11 Beyond the examples in Fig. 17.10, there are...Ch. 17 - 17.12 An investigator has reported the data...Ch. 17 - An investigator has reported the data tabulated...Ch. 17 - 17.14 It is known that the data tabulated below...Ch. 17 - 17.15 The following data are...Ch. 17 - Given these data x 5 10 15 20 25 30 35 40 45 50 y...Ch. 17 - 17.17 Fit a cubic equation to the following...Ch. 17 - Use multiple linear regression to fit x1 0 1 1 2 2...Ch. 17 - Use multiple linear regression to fit x1 0 0 1 2 0...Ch. 17 - Use nonlinear regression to fit a parabola to the...Ch. 17 - 17.21 Use nonlinear regression to fit a...Ch. 17 - 17.22 Recompute the regression fits from Probs....Ch. 17 - Develop, debug, and test a program in either a...Ch. 17 - A material is tested for cyclic fatigue failure...Ch. 17 - The following data show the relationship between...Ch. 17 - 17.26 The data below represents the bacterial...Ch. 17 - The concentration of E. coli bacteria in a...Ch. 17 - 17.28 An object is suspended in a wind tunnel and...Ch. 17 - 17.29 Fit a power model to the data from Prob....Ch. 17 - Derive the least-squares fit of the following...Ch. 17 - 17.31 In Prob. 17.11 we used transformations to...
Additional Engineering Textbook Solutions
Find more solutions based on key concepts
Analytic Functions. Find fz=ux,y+ivx,y with u or v as given. Check by the Cauchy Reimann equations for analyti...
Advanced Engineering Mathematics
(a) Show that (x) = x2 is an explicit solution to xdydx = 2y on the interval (, ). (b) Show that (x) = ex x is...
Fundamentals of Differential Equations (9th Edition)
|4.2| = ?
Basic Technical Mathematics
True or False? Explain.
1. Any set of ordered pairs is a function.
College Algebra (6th Edition)
Find E(X) for each of the distributions given in Exercise 2.1-3.
Probability And Statistical Inference (10th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- 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 5arrow_forwarda) b) c) Use composite Simpson's rule to estimate xe*dx with n=4. Subsequently, find the absolute error. dy dx Given 3y + 2x, where y(0) = 1 and h = 0.2. Approximate the solution for the differential equation for one iteration only by using Runge Kutta method of order two. Set up the Gauss-Siedel iterative equations the following linear system: 6x₁-3x₂ = 2 -x₁ + 3x₂ + x3 =1 x₂ + 4x₂ = 3 (Do not solve)arrow_forwardTable Error function (erf) values erf (z) erf (2 erf (z) 0.55 0.5033 13 0.9340 0.025 0.0282 O 60 0.6039 14 0.9523 0.05 0.0564 0.05 0 6420 15 0.9001 0.10 0.1125 0.70 0 6778 0.9703 16 0.15 0.1080 0.75 0.7112 1.7 0.9838 0 20 0.2227 080 07421 18 0.0091 025 0 2703 0.85 0.7707 1.9 0.0028 0.30 0.3290 0.90 0.7969 20 0.9953 0.35 03704 0.95 0.8200 22 0.9981 040 0.4284 O 8427 O 8802 1.0 24 0.9903 0.45 0.4755 11 2.6 0.0098 0 50 0.5205 12 0.9103 28 0 9990 A 1010 steel is to be carburized using a gas atmosphere that produces 1.0% Cat the surface of the steel. The case depth is defined as the distance below the surface that contains at least 0.5% Č. If carburizing is done at 1000 C, determine the time required to produce a case depth of 0 234 mm. For the diffusion of Garbon in FCC iron Q - 137.7 kJ/mol and Do = 0.23 x 10 m²/s. The gas constant is R- 8.314 J/(mol - K). Assume that the diffusion coefficient D remains constant and the concentrations of the diffusing atoms at the surface (c.) and at…arrow_forward
- Hello Sir.Good night.Permission, i have a question in my homework related numerical methods lesson. The following bellow is question. Please advice. Thank you so much Regards,Irfan Mention the types of problems that exist in the field of engineering, especially mechanical engineering that can be solved by the linear regression methodarrow_forwardCalculate the value of the first order derivative at the point x=0.2 with a single finite difference formula using all the following values. 0.1 0.2 0.3 0.4 f(x) 0.000 000 0.078 348 0.138 910 0.192 916 0.244981arrow_forwardConsider the function p(x) = x² - 4x³+3x²+x-1. Use Newton-Raphson's method with initial guess of 3. What's the updated value of the root at the end of the second iteration? Type your answer...arrow_forward
- 2. Solve the following ODE in space using finite difference method based on central differences with error O(h). Use a five node grid. 4u" - 25u0 (0)=0 (1)=2 Solve analytically and compare the solution values at the nodes.arrow_forwardUsing trapezoidal rule integration with 2 equal sized sub-intervals, find the area under the curve defined by the polynomial y = 0.10x5 + 0.1x³ + 24 between limits of 4.2 and 11.1. Give your answer to a precision of at least 3 significant figures. Your Answer:arrow_forwardb) In an engine design, a pair of bearing is designed to carry low load. If the lifetime of the pair of identical gear obey Weibull distribution with random with parameter a=0.0002 and B=0.5. %23 (b) Find the probability that both bearings functions properly at least 6000 hours. ::. :.arrow_forward
- 4. Solve the 2D Laplace's equation on a square domain using finite difference method based on central differences with error O(h2). Use four nodes in each direction. 0 (1.y)--5 (2.1) 0arrow_forwardUse bisection to determine the drag coefficient needed so that an 80-kg parachutist has a velocity of 36 m/s after 4 s of free fall. Note: The acceleration of gravity is 9.81 m/s2 . Start with initial guesses of xl = 0.1 and xu = 0.2 and iterate until the approximate relative error falls below 2%.arrow_forwardyo 9:1V i %A LO äbä 20 A ladder 13 ft long is leaning against a wall. The bottom of the ladder is being pulled away from the wall at the constant rate of 6 ft/min. How fast is the top of the ladder moving down the wall when the bottom of the * ?ladder is5 ft from the wall 13 y 6 ft/min 2.5 3.5arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305387102/9781305387102_smallCoverImage.gif)
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY