Exam 2 Grading method
Posted: Wed Nov 10, 2010 2:23 pm
- Problem 1.
Part a)
- 5 pts for correct assumption of the form of x and calculation of x_dot
- 5 pts for work including substitution into given equation and reducing to single variable
- 5 pts for proper recursive form
Part b)
- 5 pts for proper exponential solution to ODE
- 5 pts for all work leading to Taylor series expansion
In most cases, 1 or 2 pts was the maximum deducted if work was shown, and in one or two instances, 3 pts was deducted when I felt there was a more significant lack of understanding displayed in the work.
In rare occasions, some parts of the problems contained no work, these parts received 0 points. - Problem 2.
+5 for 3 initial assumptions
+5 ended up with a2 = 0 (using a correct method)
+10 for the recursion reconstruction equation, with steps shown (minus 1-2 pts for slight math errors)
+5 for all 6 correct terms - Problem 3.
(5) Singular point
(5) Regular singular point (1pt for yes; 4 pts for why)
(5) Correct series representation of x
(10) Calculations - Problem 4.
(5) Series representation of x
(5) Collect of t^n on LHS
(15) Calculation of a_0, a_1, a_2, a_3, a_{n+2}
Notes:
(10) Correct representation of a_{n+2}
(5) Other calculations and final answer