MAE 284 FINAL EXAM 2022 LATEST UPDATE

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MAE 284 FINAL EXAM 2022 LATEST UPDATE All mathematical problems have closed-form solution(i.e. they can be solved for a variable having to make guesses) (T/F) - answerFalse All variables that have... been defined are found in the command window, even empty ones(T/F) - answerFalse Anonymous functions need to be defined before being used(T/F) - answerTrue Given two vectors a and b, which command would you use to calculate the cross product of a and b? - answercross(a,b) The bisection algorithm is an open method(T/F) - answerFalse The bisection method is most effective when there are multiple roots inside a bracket (T/F) - answerFalse A false position method is based on the false assumption that the function can be approximated by a(n) - answerstraight line One disadvantage of the Newton-Raphson method is that it requires the user to analytically find the derivative of the function(T/F) - answerTrue For the fourth iteration in the Newton-Raphson method, you will use the estimated root location from the third iteration as the new initial point(T/F) - answerTrue This study source was downloaded by 100000851714074 from CourseHero.com on 09-09-2022 15:57:26 GMT -05:00 https://www.coursehero.com/file/163854708/MAE-284-FINAL-EXAM-2022-LATEST-UPDATEpdf/ MATH Which one of the following functions can be used to find the list of the lower bound and upper bound that bracket a root? - answerincsearch Quadrature is another name for integration(T/F) - answerTrue The key to Guass Quadrature is to balance the function values(T/F) - answerFalse The trapezoidal rule approximates the function by a: - answerstraight line The Guass Quadrature formulas we discussed in class are called Guess-Legendre formulas.(T/F) - answerTrue Romberg's method is NOT a newton-Cotes method.(T/F) - answerFalse Simpsons 3/8 rule approximates the function by a _____ order polynomial - answerThird The composite Simpson's 1/3 rule requires the number of segments be: - answerEven The key to Guass Quadrature is to balance the positive and negative errors.(T/F) - answerTrue Naive Guass elimination ensures that division by zero is not possible(T/F) - answerFalse If the determinant of a matrix is zero, the inverse of the matric is a scalar.(T/F) - answerFalse If two rows of a matrix are identical, the determinant is zero.(T/F) - answerTrue If one row of a matrix consists entirely of zeros, then the determinant is zero(T/F) - answerTrue This study source was downloaded by 100000851714074 from CourseHero.com on 09-09-2022 15:57:26 GMT -05:00 https://www.coursehero.com/file/163854708/MAE-284-FINAL-EXAM-2022-LATEST-UPDATEpdf/ A system of equations can be written in the form: Ax=b, where A is a square matrix, x is a vector of unknowns, and b is a vector of constants (T/F) - answerTrue The general form of a first order ODE is dy/dt = f(t,y) (T/F) - answerTrue Which of the following affect the stability of numerical methods used to solve ODEs? - answerThe differential equation, the step size, the numerical method Which of the following is based on using the average for two slopes of the solution of the ODE to calculate the value of the solution at the next point? - answerHuen Multiple applications of the predictor and corrector steps will not improve the accuracy of the solution(T/F) - answerFalse In general, which of the following will take more time to calculate the solution for a stiff system? - answerAn explicit adaptive algorithm(ode45) Eigenvalues indicate how fast a stable mode decays since the response can be written as x(t)=Ce^ht (T/F) - answerTrue Which of the following corresponds to a system that oscillates? - answerUnderdamped The domain of a finite difference problem with boundary conditions specified is divided into 10 sections. How many nodes are there? How many unknowns are there? - answer11,9 What technique did we use to solve nonlinear finite-difference equations? - answerGuass-Seidel The finite difference method is based on converting continuous derivatives algebraic This study source was downloaded by 100000851714074 from CourseHero.com on 09-09-2022 15:57:26 GMT -05:00 https://www.coursehero.com/file/163854708/MAE-284-FINAL-EXAM-2022-LATEST-UPDATEpdf/ approximations(T/F) - answerTrue Partial differential equations have more than one independent variable(T/F) - answerTrue Initial value problems have all necessary conditions given at a single value of the independent variable. (T/F) - answerTrue The only way to increase the accuracy of a numerical approximation of a derivative is to add more terms in the Taylor Series used to derive the approximation(T/F) - answerFalse In general, ____________ the step size, h, will decrease the error in a numerical approximation of a derivative. - answerDecreasing There are three types of numerical derivative approximations: forward, backward, and centered(T/F) - answerTrue The equal sign, =, is used to assign data to a variable(T/F) - answerTrue How many inputs are in the following function? [a,b] = quiz1(c,d,e,f,g) - answer5 The roots of a function f(x) are located at the points where the function crosses the x-axis(T/F) - answerTrue Bracketing methods always converge, but usually do so more slowly than open methods(T/F) - answerTrue The false position algorithm is identical to the bisection algorithm, except for the calculations for the estimated root location(T/F) - answerTrue This study source was downloaded by 100000851714074 from CourseHero.com on 09-09-2022 15:57:26 GMT -05:00 https://www.coursehero.com/file/163854708/MAE-284-FINAL-EXAM-2022-LATEST-UPDATEpdf/ A bracket with opposite-signed function values always contains exactly one root(T/F) - answerFalse The secant method is similar to the Newton-Raphson method, but uses an approximation of the derivative(T/F - answerTrue The secant method requires two initial estimates, but they are not required to bracket the root(T/F) - answerTrue The main advantage of the secant method over the Newton-Raphson method is that the secant method only requires analytically finding one derivative(T/F) - answerFalse The main disadvantage of the newton raphson method is that it may not converge(T/F) - answerTrue MATLAB's built in fzero function can be used to find the roots, if any, of an equation of the form f(x)=c (T/F) - answerTrue Which of the following function will import a data file? - answerimportdata ... 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