Incompetent Math Professor: How to Confront Your Diff Eq Instructor

[omagdon7]

I am currently enrolled in a Diff Eq course at a community college. My instructor has an MS in Math and Electrical engineering which I assumed meant he knew how to think but apparently he doesn't.

The problem is this, we are solving differential equations using the LaPlace Transform for differential equations with non-constant coefficients. So on the board he does the LaPlace transform just fine, but when it comes to partial fractal decomposition to solve the actual differential equation he insists that if the factor in the denominator is a prime quadratic we do not need an Ax+B term. He says that unlike in calculus where we wanted to integrate something that we only need a constant term. This to me seems to be completely ludicrous because you cannot set two things equal which are not equal so when you solve the inverse LaPlace you get an answer that is not relevant to your initial problem.

Firstly, I am correct that you are not allowed to do what he is doing (throwing away the Ax term) and secondly, if so how do I tell him without upsetting him.

 

[Antiphon]

Can't help you without seeing the actual equations.

 

[matt grime]

try explinaing what a "prime quadratic" is, cos I'm buggered if i know. (lecturers are rarely incompetent, and i give the benefit of the doubt to them and not the student. you may wish to bear in mind that the best help you will get here will be from people who teach and not those in the classes so be careful or we (well, me at any rate) may not bother to help you if you use such unsubstantiated claims and blame shifting. ad hominem attacks on them are almost always unjustified)

 

[HallsofIvy]

If you are saying that you have factor in the denominator of the form x²+ a which cannot be factored, then it is correct that your partial fraction expansion must include a term of the form (Ax+B)/(x²+a) with both A and B. As to how you would convince him of that, I would suggest that you do an example and show that the Ax term is necessary in order to be able to write it in partial fraction form. You should do that carefully of course. Perhaps, show him your solution with the Ax term and ask if he would please show you how to do that problem his way. If he does come up with an answer, it should be relatively simple to determine if that solution does or does not in fact satisfy the orginal differential equation.

 

[learningphysics]

Can you post an example and show exactly how he did the problem?

 

[omagdon7]

It is exactly as Halls of Ivy posted the denominator is a prime quadratic. The actual quadratic was (S^2+1) I don't know how to format the equations properly so I apologize. The instructor was insistent there didn't need to be an Ax term in the numerator and then finally 40 minutes into the class, he made some crap up about how because (S^2+1)=(S-0)^2+(1^2) that then and only in this one case did we need to have an Ax term in the numerator. He made up some complete horsecrap about how it was a completed square to justify this and proceeded to be unable to finish the problem anyways. It took him 40 minutes to find the numerators because he tried to do it using the method of plugging in values of x to make part of the system go to 0 i.e. if you had A(x+2)(x-3) + B(x+1)=7 plugging in either a -2 or a 3 to eliminate A and solve for B, unfortunately all the monomials were prime quadraticsinstead of eliminating several variables he ended up having to use several values of x and then having to solve 4 simulataneous equations in 4 variables. It was just very frustrating as even with my limited knowledge I solved the equations before he finished doing the LaPlace transform.

 

[CaptainQuaser]

"lecturers are rarely incompetent, and i give the benefit of the doubt to them and not the student."

Yes, I have only ever had one incompetant prof, and his incompetence was not in the subject matter (Calculus) but his ability to express it (in english). If a university prof is saying something, especially at lower level classes (undergrad) I would say it's a safe bet that its true. Try going to his office and having him explain it to you, profs are often more than happy to help students understand the material if they take the time to go see them.

 

[omagdon7]

No he is definitely without a doubt wrong like honestly it isn't possible that what he's saying is true. His claim is that F(x)/((x^2+1)^2)=A/(x^2+1) + B/(x^2+1)^2 where F(x) is a third order polynomial (not that it matters). In some cases it may be true, as the term that should have an x in it could be 0. However, as a generalization by definition it is not true, it is simple high school algebra. He is a professor at a community college if it makes any difference in the stories credulity. The story is exactly as how HallsofIvy interpreted it.

 

[Brad Barker]

"lecturers are rarely incompetent, and i give the benefit of the doubt to them and not the student."

Yes, I have only ever had one incompetant prof, and his incompetence was not in the subject matter (Calculus) but his ability to express it (in english). If a university prof is saying something, especially at lower level classes (undergrad) I would say it's a safe bet that its true. Try going to his office and having him explain it to you, profs are often more than happy to help students understand the material if they take the time to go see them.

this is the rare case when the professor is definitely wrong.

yeah, do what halls of ivy suggested.

 

[EnumaElish]

Maybe he was distracted, anxious, momentarily confused, in need of a sip of water, sleep deprived, cold under A/C turned up way too high, caffeine withdrawn, assaulted by warm and humid weather conditions, hungry, angry, tired, impatient, still suffering from the lunch he ate, missed lunch, missed breakfast, had a car accident, without a car so he had to walk or even worse take the bus to school, with girlfriend blues, having family problems, human.

 

[GCT]

my differential equations professor was chinese, throughout the whole semester I didn't understand a thing he said (just finished it this summer). I think that the basic assumptions of most asian mathematicians is that mathematics is practical, you don't really need to supplement language to understand or explain it...it's somewhat of a language in and of itself.

 

[EnumaElish]

my differential equations professor was chinese, throughout the whole semester I didn't understand a thing he said (just finished it this summer). I think that the basic assumptions of most asian mathematicians is that mathematics is practical, you don't really need to supplement language to understand or explain it...it's somewhat of a language in and of itself.

There have to be exceptions where you have to express an idea through language. Are you sure he never even wrote English phrases on the board, as in "a unique line goes through two points in space"?

 

[learningphysics]

Yes, he's definitely wrong. I think you should definitely talk to him... but be careful about it. Show him that A/(x^2+1) + B/(x^2+1)^2 = [Ax^2 + (A+B)]/(x^2+1)^2 so a third order polynomial is impossible in the numerator. Hopefully that will be enough.

 

[GCT]

There has to be exceptions where you have to express an idea through language. Are you sure he never even wrote English phrases on the board, as in "a unique line goes through two points in space"?

no phrases, simply terms

 

[matt grime]

Please understand that I am doing this to make a point not because I am a pedant (I am a pedant but that isn't why I'm about to do this; my typing is too awful to actually be this fussy without actually being a hypocrite.

No he is definitely without a doubt

pleonasm or needs bracketing commas

wrong like honestly it isn't possible that what he's saying is true.

needs punctuating, unnecessary use of the word 'like'

His claim is that F(x)/((x^2+1)^2)=A/(x^2+1) + B/(x^2+1)^2 where F(x) is a third order polynomial (not that it matters). In some cases it may be true, as the term that should have an x in it could be 0. However, as a generalization by definition it is not true, it is simple high school algebra. He is a professor at a community college if it makes any difference in the stories

story's, not stories, one is possesive; one is plural

credulity. The story is exactly as how HallsofIvy interpreted it.

HOw about if I were to label you literately incompetent? Not nice is it?

You need to understand that standing in front of an audience that is provably hostile is not an easy undertaking. People make mistakes, especially in maths. You don't believe me? Try teaching a clas someday. If you want to be helpful to him and the rest of the class talk to him privately; any good teacher will be happy to correct his mistake. Remember, this person may well be teaching a course that they have no interest in but need to do in order to satisfy their teaching requirements. It doesn't help to label them incompetent. Think: has he actually done anything "incompetent" in describing Laplace transforms or are his errors in things as inconsequential as not doing partial fractions in the fastest way? Because one of these is important the other is merely bookwork.

 

[Brad Barker]

what was the point of proofing the original post?


anyway, i just remembered that in my class, we didn't do decomposition into partial fractions that way.

a completely accurate and alternative method is to factor the denominator that is unfactorable in the real number system... in the complex number system!

you'll end up with, in general, a polynomial multiplied by an exponential with a complex argument.

then you use euler's formula and the complex parts will usually take care of themselves.

and this should give you the same answer as the Ax+B/(ax^2+b) method. but it's cooler.

just lettin' you know.

 

[matt grime]

what was the point of proofing the original post?

to indicate that it is easy to criticize (especially things that are pretty irrelevant); that, based upon that criticism, to declare someone as incompetent is not necessarily helpful or constructive; that it may not induce a particularly pleasant feeling if you are the one labelled as incomptent.

and i did also imply that corrections of internet posts are not something i condone in general: it would be hypocritical to say the least.

if you want to say that 'i think my lecturer made a mistake, how should i go about correcting it?' fine, but to needlessly label them as incompetent based upon not doing partial fraction decomposition as succinctly as can be done is, frankly, leaping to an insulting conclusion. such attitudes only lead to a hostility amongst the teaching fraternity to what they see as unappreciative students.

 

[Eratosthenes]

I am currently enrolled in a Diff Eq course at a community college. My instructor has an MS in Math and Electrical engineering which I assumed meant he knew how to think but apparently he doesn't.

The problem is this, we are solving differential equations using the LaPlace Transform for differential equations with non-constant coefficients. So on the board he does the LaPlace transform just fine, but when it comes to partial fractal decomposition to solve the actual differential equation he insists that if the factor in the denominator is a prime quadratic we do not need an Ax+B term. He says that unlike in calculus where we wanted to integrate something that we only need a constant term. This to me seems to be completely ludicrous because you cannot set two things equal which are not equal so when you solve the inverse LaPlace you get an answer that is not relevant to your initial problem.

Firstly, I am correct that you are not allowed to do what he is doing (throwing away the Ax term) and secondly, if so how do I tell him without upsetting him.

Well you it seems you have two choices.

1. Go to his office and ask him about it, but be nice. Remember he is your teacher.

2. Don't do anything. Then on the next exam if he marks something wrong that is correct you can go ask him about it.


In the end it will work itself all out. Goodluck and try not to worry about it:).

 

[Moonbear]

I'll leave the judgement as to whether the method is or is not an acceptable method (even if not the most efficient or fastest) to the math experts around here, but I will point out that sometimes something that appears to be a long way around solving something in a class is intentionally done that way because it leads up to something else in the lesson plan, and sometimes it's to expose you to an alternative method of doing something when the easy/obvious way is, well, obvious if you've paid attention in your previous courses.

Just because you know of another, faster way to solve a problem, don't assume your professor is incompetent or doesn't have a method to his madness. The best approach is to assume there is a good reason for the way he has demonstrated the problem that you have missed, and ask him in his office hours to explain why he taught that particular approach and to please explain more clearly to you how to do it and if it would be okay for you to use your method on an exam (some professors aren't testing on your final answer, but on the method you use to get to it). If it turns out that he explained it incorrectly, having asked him the right way will encourage him to correct that in the next class for everyone, and if he has explained a perfectly acceptable method, albeit a more tedious one, for a particular reason, you will also find out what it is if you ask.

 

[Brad Barker]

I'll leave the judgement as to whether the method is or is not an acceptable method (even if not the most efficient or fastest) to the math experts around here, but I will point out that sometimes something that appears to be a long way around solving something in a class is intentionally done that way because it leads up to something else in the lesson plan, and sometimes it's to expose you to an alternative method of doing something when the easy/obvious way is, well, obvious if you've paid attention in your previous courses.

Just because you know of another, faster way to solve a problem, don't assume your professor is incompetent or doesn't have a method to his madness. The best approach is to assume there is a good reason for the way he has demonstrated the problem that you have missed, and ask him in his office hours to explain why he taught that particular approach and to please explain more clearly to you how to do it and if it would be okay for you to use your method on an exam (some professors aren't testing on your final answer, but on the method you use to get to it). If it turns out that he explained it incorrectly, having asked him the right way will encourage him to correct that in the next class for everyone, and if he has explained a perfectly acceptable method, albeit a more tedious one, for a particular reason, you will also find out what it is if you ask.

nope, sorry. the guy is wrong.

i think it's less of an issue of incompetence and more of an issue of him not reviewing that part of calc II--it's probably been a while since he's had to do partial fraction decomposition. (though, i think it's pretty irresponsible to teach something that you haven't reviewed.)

 

[Moonbear]

nope, sorry. the guy is wrong.

i think it's less of an issue of incompetence and more of an issue of him not reviewing that part of calc II--it's probably been a while since he's had to do partial fraction decomposition. (though, i think it's pretty irresponsible to teach something that you haven't reviewed.)

It is irresponsible, but sometimes human. He may have had this course thrust upon him at the last minute and just didn't have time to review properly before needing to teach that lecture. In any case, even if he's wrong, the best way to bring it to his attention is to ask as if it is you who doesn't understand his explanation rather than that his explanation was wrong. It's just the best way to avoid creating hard feelings. Who knows, if you ask him and he realizes you're actually paying attention in his class, you might build a good rapport with him that will pay off when you need a recommendation some day.