Solutions for EBK NUMERICAL METHODS FOR ENGINEERS
Problem 1P:
10.1 Use the rules of matrix multiplication to prove that Eqs. (10.7) and (10.8) follow from Eq....Problem 2P:
10.2 (a) Use naive Gauss elimination to decompose the following system according to the description...Problem 3P:
10.3 (a) Solve the following system of equations by LU decomposition without pivoting
(b) ...Problem 4P:
10.4 Solve the following system of equations using LU decomposition with partial pivoting:
Problem 5P:
Determine the total flops as a function of the number of equations n for the (a) decomposition, (b)...Problem 6P:
Use LU decomposition to determine the matrix inverse for the following system. Do not use a pivoting...Problem 7P:
10.7 Perform Crout decomposition on
Then, multiply the resulting and matrices to determine...Problem 8P:
The following system of equations is designed to determine concentrations (thecsing/m3) in a series...Problem 10P:
10.10 (a) Determine the LU decomposition without pivoting by hand for the following matrix and check...Problem 12P:
Determine Ae,A1,andAfor [A]=[82109131516] Scale the matrix by making the maximum element in each row...Problem 13P:
10.13 Determine the Frobenius and the row-sum norms for the systems in Probs. 10.3 and 10.4. Scale...Problem 14P:
10.14 A matrix is defined as
Using the column-sum norm, compute the condition number and how...Problem 15P:
10.15 (a) Determine the condition number for the following system using the row-sum norm. Do not...Problem 16P:
10.16 Determine the condition number based on the row-sum norm for the normalized Hilbert matrix....Problem 17P:
Besides the Hilbert matrix, there are other matrices that are inherently ill-conditioned. One such...Problem 18P:
10.18 Develop a user-friendly program for LU decomposition based on the pseudocode from Fig. 10.2.
Problem 19P:
Develop a user-friendly program for LU decomposition, including the capability to evaluate the...Problem 20P:
Use iterative refinement techniques to improve x1=2,x2=3,andx3=8, which are approximate solutions of...Problem 21P:
10.21 Consider vectors:
Vector is perpendicular to as well as to. It is also known that. Use...Problem 22P:
10.22 Consider the following vectors:
Where is an unknown vector. If
use any method learned...Problem 23P:
10.23 Let the function be defined on the interval as follows:
Determine the constants a, b, c,...Browse All Chapters of This Textbook
Chapter 1 - Mathematical Modeling And Engineering Problem SolvingChapter 2 - Programming And SoftwareChapter 3 - Approximations And Round-off ErrorsChapter 4 - Truncation Errors And The Taylor SeriesChapter 5 - Bracketing MethodsChapter 6 - Open MethodsChapter 7 - Roots Of PolynomialsChapter 8 - Case Studies: Roots Of EquationsChapter 9 - Gauss EliminationChapter 10 - Lu Decomposition And Matrix Inversion
Chapter 11 - Special Matrices And Gauss-seidelChapter 12 - Case Studies: Linear Algebraic EquationsChapter 13 - One-dimensional Unconstrained OptimizationChapter 14 - Multidimensional Unconstrained OptimizationChapter 15 - Constrained OptimizationChapter 16 - Case Studies: OptimizationChapter 17 - Least-squares RegressionChapter 18 - InterpolationChapter 19 - Fourier ApproximationChapter 20 - Case Studies: Curve FittingChapter 21 - Newton-cotes Integration FormulasChapter 22 - Integration Of EquationsChapter 23 - Numerical DifferentiationChapter 24 - Case Studies: Numerical Integration And DifferentiationChapter 25 - Runge-kutta MethodsChapter 26 - Stiffness And Multistep MethodsChapter 27 - Boundary-value And Eigenvalue ProblemsChapter 28 - Case Studies: Ordinary Differential EquationsChapter 29 - Finite Difference: Elliptic EquationsChapter 30 - Finite Difference: Parabolic EquationsChapter 31 - Finite-element MethodChapter 32 - Case Studies: Partial Differential Equations
Sample Solutions for this Textbook
We offer sample solutions for EBK NUMERICAL METHODS FOR ENGINEERS homework problems. See examples below:
Chapter 1, Problem 1PChapter 1, Problem 12PChapter 1, Problem 22PChapter 2, Problem 1PChapter 2, Problem 14PChapter 2, Problem 18PChapter 3, Problem 1PChapter 3, Problem 11PChapter 4, Problem 1P
Chapter 4, Problem 6PChapter 5, Problem 1PChapter 5, Problem 3PChapter 5, Problem 4PChapter 6, Problem 1PChapter 6, Problem 2PChapter 6, Problem 7PChapter 6, Problem 23PChapter 7, Problem 1PGiven Information: The given equation is, f(x)=x3+x2−4x−4 Use Müller’s method. Formula used: The...Chapter 7, Problem 9PChapter 8, Problem 1PChapter 8, Problem 23PChapter 8, Problem 44PChapter 8, Problem 46PChapter 8, Problem 48PChapter 9, Problem 1PChapter 9, Problem 2PChapter 9, Problem 21PChapter 10, Problem 1PChapter 10, Problem 3PChapter 10, Problem 8PChapter 11, Problem 1PChapter 11, Problem 12PChapter 11, Problem 13PChapter 12, Problem 1PChapter 12, Problem 10PChapter 12, Problem 12PGiven Information: The air flow through the room with proper description is provided as follows:...Chapter 13, Problem 1PChapter 13, Problem 6PChapter 13, Problem 8PChapter 14, Problem 1PChapter 14, Problem 5PChapter 15, Problem 1PGiven Information: The factors are given as below, Resource Regular Premium Supreme Resource...Chapter 16, Problem 1PChapter 16, Problem 5PChapter 16, Problem 19PChapter 16, Problem 33PChapter 17, Problem 1PChapter 17, Problem 2PChapter 17, Problem 22PChapter 18, Problem 1PChapter 18, Problem 10PChapter 18, Problem 14PChapter 19, Problem 1PChapter 19, Problem 4PChapter 19, Problem 6PChapter 20, Problem 1PGiven Information: The table is given as, Depth, m 0 0.5 1.0 1.5 2.0 2.5 3.0 Temperature, Celsius 70...Chapter 20, Problem 15PChapter 20, Problem 16PChapter 20, Problem 41PChapter 20, Problem 48PChapter 20, Problem 60PChapter 21, Problem 1PChapter 21, Problem 2PChapter 22, Problem 1PGiven Information: The given integral is, ∫2∞1x(x+2)dx Formula used: Simpson’s 1/3 rule. I1=h3[...Chapter 23, Problem 1PChapter 23, Problem 8PChapter 23, Problem 20PChapter 24, Problem 1PChapter 24, Problem 35PChapter 24, Problem 36PChapter 24, Problem 44PChapter 24, Problem 45PChapter 24, Problem 46PChapter 25, Problem 1PChapter 25, Problem 2PChapter 26, Problem 1PChapter 26, Problem 6PChapter 27, Problem 1PChapter 27, Problem 27PChapter 27, Problem 28PChapter 27, Problem 29PChapter 28, Problem 1PChapter 28, Problem 7PGiven Information: The series of first order, liquid phase reactions is, A→k1B→k2C The second order...Chapter 28, Problem 18PChapter 28, Problem 27PChapter 28, Problem 49PChapter 29, Problem 1PGiven Information: The fixed temperature at top and right boundary is 100 °C and the fixed...Chapter 30, Problem 1PChapter 30, Problem 5PChapter 31, Problem 1PGiven Information: To develop nodal equations for the temperature and their gradients at each of the...Chapter 32, Problem 1PChapter 32, Problem 9P
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Numerical Methods For Engineers With Personal Computer Applications
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