practiceExam1Sample1

practiceExam1Sample1 - 1 Please answer the questions below...

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1. Please answer the questions below by selecting either (a) one of the answers provided. i. The following orders can be included in a Taylor Series Expansion of a non-linear function to generate a linear approximation for the function: a. 0 th order b. 1 st order c. 2 nd order d. Both 0 th and 1 st order e. The 0 th , 1 st , and 2 nd order terms can all be included ii. A Taylor Series approximation for a function which includes the 0 th and 1 st order terms will have an error that is on the order of the step size raised to what power: a. 0 b. 1 c. 2 d. 3 e. None of the above iii. Which of the following statements concerning Gaussian Elimination methods for solving linear systems of equations (i.e. Ax=b) is true: a. Gaussian elimination requires more computations than does using the matrix inverse method to compute x=A -1 b. b. Partial pivoting should generally be used to help avoid division by zero errors and round-off errors during elimination. c. Gauss-Jordan is more computationally efficient than is Gaussian elimination with back substitution. d. Scaling helps to eliminate round-off errors when two coefficients in the same equation are of dramatically different magnitudes. iv. You form an ODE initial value problem for a chemical reaction. One reaction rate is very fast and another is very slow. You have the choice of using an implicit method or an explicit method.
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