final

To solve a system of ordinary differential equations with the simplest algorithm, we must use
Euler’s method.
a. True.
b. False.

a

2. Finding the derivative at a series of data points with the highest accuracy.
   a. Forward divided difference
   b. Backward divided difference
   c. Centered divided difference
   d. Newton's divided difference

c

3. Root-finding: Estimating data points in between the data that have already been collected.
   a. True.
   b. False.

b

4. Linear regression: Finding the vector [x] that satisfies [A][x] = [b].
   a. True.
   b. False.

b

5. Find the area-under-the-curve for a series of data points, with the highest accuracy.
   a. Sum of squares.
   b. Simpson's 3/8 rule.
   c. Simpson’s 8/3 rule.
   d. Trapezoidal rule.

b

6. Finding the maximum of a multi-dimensional function f(x,y), where you can find its
   derivative but not its second derivative, you use Steepest ascent method.
   a. True.
   b. False.

a

7. Based on Taylor series, for f(x) = 1.2 - 0.25x - 0.5x2 - 0.15x3 from xi = 0, the 1st order
   approximation at xi+1 = 1 is:
   a. 0.95
   b. 0.25
   c. 1.2
   d. 1.45

a

8. Based on measurements of x = 2 ± 0.1 and y = 3 ± 0.5, the expected error in f = 3xy2 is:
   a. 54
   b. 0.075
   c. 20.7
   d. 0.6

c

9. When would roundoff error be a concern?
   a. Adding numbers with very similar magnitudes
   b. Subtracting numbers with very similar magnitudes
   c. Using lower-order approximations
   d. Using large step sizes

b

10. Which of the following is an advantage of the 4th order Runge Kutta method vs. Euler’s
    method?
    a. Less roundoff error
    b. Simpler mathematical form
    c. Faster comptutation
    d. Less truncation error

d

11. Error propagation can be used to calculate the range of error due to:
    a. Measurement error
    b. Roundoff error
    c. True error
    d. Relative error

a

12. When performing Gaussian Elimination, if the first value of A is zero, then, partial pivoting
    is required
    a. True.
    b. False.

a

13. Which method of numerical integration is most accurate for 4 evenly spaced points?
    a. Trapezoidal rule
    b. Simpson’s 1/3 rule
    c. Simpson’s 3/8 rule
    d. Euler’s method
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