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SOLUTIONS MANUAL FOR APPLIED NUMERICAL METHODS WITH MATLAB FOR ENGINEERS AND SCIENTISTS 5TH EDITION BY STEVEN CHAPRA (ALL CHAPTERS 100% ORIGINAL EXAM WITH ACTUAL QUESTIONS AND COMPLETE 100%CORRECT ANSWERS WITH VERIFIED AND WELLEXPLAINED RATIONALES ALREA

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SOLUTIONS MANUAL FOR
APPLIED NUMERICAL METHODS
WITH MATLAB FOR ENGINEERS
AND SCIENTISTS 5TH EDITION BY
STEVEN CHAPRA (ALL
CHAPTERS 100% ORIGINAL
EXAM WITH ACTUAL
QUESTIONS AND COMPLETE
100%CORRECT ANSWERS WITH
VERIFIED AND WELLEXPLAINED
RATIONALES ALREADY GRADED
A+ BY EXPERTS |LATEST
VERSION 2024 WITH
GUARANTEED SUCCESS AFTER
DOWNLOAD ALREADY
PASSED!!!!!!! (PROVEN ITS ALL
YOU NEED TO EXCEL IN YOUR
EXAM

,1

, CHAPTER 1

Model coefficients in a nonlinear equation of the form
y= a1xe^(a2x^2)
can be determined using which of the following algorithms
- General linear least squares
- Linear regression using the linearized data and linearized model
- Nonlinear regression
Which of the following methods can be applied to the solution of nonlinear systems of equations.

1 - Gauss-Seidel Iteration
2 - Newton-Raphson Iteration
3 - Gaussian Elimination
4 - Successive Substitution
5 - LU Factorization
6 - Jacobi iteration
- Newton-Raphson Iteration

- Successive Substitution
Newton-Raphson iteration is to be used to solve the following system of equations:
x^2 = 5-y^2
y+1 = x^3
Calculate the elements of the Jacobian matrix (to 2 decimal places) if the values of x and y in the current
iteration are x = 1 and y = 1.5. Rearrange the equations to formulate the roots problems so that the
constants (5 in the first equation and 1 in the second equation) are positive before taking the partial
derivatives.
J_11 = -2
J_12 = -3
J_21 = -3
J_22 = 1
Which of the following are statistics that indicate the quality of a curve fit? (Select all that apply)

1 - Mean of the data
2 - Euclidean norm of the residuals with respect to the model
3 - Standard deviation
4 - Standard error of the estimate
5 - Curve fit coefficients
6 - Coefficient of determination
2,4,6
The coefficient of determination (r2) for a "good" fit will be
Close to but not exceeding 1
In the general linear least squares formulation, the _________ functions can be any function of the
independent variable(s), but can not include the fit coefficients.
Basis

2

, You have performed a curve fit to a data set using nonlinear regression. The standard error of the curve fit
is 0.5. Which of the following statements is(are) accurate?
We can expect the model to predict the data to within +/- 1.0 approximately 95% of the time.

We can expect the model to predict the data to within +/- 0.5 approximately 68% of the time.
The Jacobian matrix can be calculated using a finite difference approach in cases where derivation of the
analytical partial derivatives is tedious. Which of the following statements is/are true about this approach?
- The approach does not introduce error into the method because the derivatives in the Jacobian are only
used to inform the guess for the next iteration.

- The accuracy of the Newton-Raphson method is ultimately determined by the stopping criterion
regardless of whether the derivatives are exact or approximated.

- The approach uses perturbation of one of the variables by a small factor (e.g. 1e-6*xi) to approximate
the partial derivatives with finite difference approximations.
The equation for the standard error must be modified depending on the number of coefficients in the
mathematical model that is being fit to the data.

T/F
True

When writing mathematical expressions involving vectors, it is often necessary to include a period before
multiplication (e.g. .*) when we desire element-by-element multiplication because (select all that apply):
-the default is matrix multiplication as defined in linear algebra, not element-by-element multiplication.

-failure to do so may result in an error.

-failure to do so may yield unexpected numerical results
Many built-in functions will accept scalars or vectors as input arguments. In general they operate element
by element when the input is a vector.
T/F
True
Below is a list of operations that may all be included in a single command. Please put these in the order by
which MATLAB evaluates them when executing the command. Note operations on the same precedence
level are executed left to right. Also, the order of operations can be overridden using parentheses.
-exponentiation (^)
-multiplication and division (* /)
-addition and subtraction (+ -)
-parentheses ()
1 - parentheses ()
2 - exponentiation (^)
3 - multiplication and division (* /)
4 - addition and subtraction (+ -)
Where you enter MATLAB commands at the prompt
Command Window
Records all previous commands
Command History

3

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