Why Is It Crucial to Check Your Work in Differential Equations?

[Brad Barker]

some professors don't really accommodate work-checking. my intro to theoretical phys professor also taught elementary differential equations and the calcs, in various years. his approach to testing was to make the test "unfinishable." most students weren't able to complete the exam or really check their answers. i'd be able to finish, but going at full-speed and without really being able to check. (my personal opinion is that this isn't very fair to the students.)


another anecdote: i got a 70-something instead of a 90-something on a four question relativity exam because i didn't read through the instructions all the way. i saw a problem that looked familiar, so i worked out what i thought the question asked and not what the question ACTUALLY asked.

so when you check your work, i guess, also take the time to re-read the instructions!

 

[mathwonk]

that is good advice about rereading the questions.

As to the time needed to finish an exam, i usually give over an hour for a test that i can finish in 8-12 minutes, and many people are still "working", i.e. scratching their heads, at the end. so how long it takes often depends on how well one knows the material.

e.g. to solve the de: y''+y'+y = 2x-x^2, note that the LHS is (1+D+D^2)y, which has inverse (1-D) modulo monomials of degree at most 2, i.e.

(1+D+D^2) (1-D)f = (1-D^3)f = f, if f is a polynomial of degree 2 or less, since D^3 f = 0 for such f.

so the answer is y = (1-D)(2x-x^2) = 2x-x^2 -2 +2x = -2+4x-x^2, which takes only a few seconds.

check: -2+4x-x^2 + 4-2x -2 = 2x-x^2. ok.

of course if one refuses to learn about operators and uses a more cumbersome method, like variation of parameters, it takes longer.

 

[amenon]

I completely agree that checking your work will do you good. But that means going back and doing the test again. That takes a long time.

 

[mathwonk]

the point is to practice taking tests before going into the test room. time yourself, and work at completing a test with checking, in less than the time alotted.

how many times have you prepared for a test by writing a sample test, longer than the one you expect, then taking it under timed conditions, and checking it?

never? what kind of student are you? you can do as well in school as you wish to do, it all depends on how much effort and time you want to expend at it.

 

[Manchot]

and many people are still "working", i.e. scratching their heads, at the end. so how long it takes often depends on how well one knows the material.

You shouldn't judge your students negatively if they take the entire period to take an exam. I almost never leave early when I'm taking an exam, though I'm almost always done early. The way I see it, if I have the time to go back and check two, three, even four times, there's no harm done in doing so.

 

[mathwonk]

you are quite right to take all the time available. i encourage my students to do this, and am disappointed when they leave early. but in this case i refer to people who did not do well even though they took more than the full amount of time.

 

[mathwonk]

i.e. i do not judge them negatively for taking a lot of time, only for taking a lkot of time and still getting a D or F ("scratching their heads").