For All Mah Dead Homies...

[ka8ncr]

...or soon to be dead homies after their calc finals.

Hope this helps!

[n2ize]

Its amazing how many people flunk calc.

[ka8ncr]

Yep. And forgetting the constant has been the difference between passing and failing an exam for more than one person.

The problem isn't necessarily calculus; the problem is really poor math instructors.

[WØTKX]

http://education-portal.com/articles/List_of_Free_Online_Calculus_Courses_and_Lessons.h tml

[ka8ncr]

http://education-portal.com/articles/List_of_Free_Online_Calculus_Courses_and_Lessons.h tml

You'd think that would make it easier, wouldn't ya?

[N7RJD]

Personally the only problem I've ever had with calc
is when the batteries died and a bad time.

Oh, you meant calculus, I though you meant people
couldn't operate calculators. I remember when the
things were damn near outlawed in school where now
they seem to teach kids to rely on them rather than teach
them how to use their head.

[NQ6U]

I never even got past algebra, so I never had the opportunity to flunk calculus.

[KC2UGV]

Personally the only problem I've ever had with calc
is when the batteries died and a bad time.

Oh, you meant calculus, I though you meant people
couldn't operate calculators. I remember when the
things were damn near outlawed in school where now
they seem to teach kids to rely on them rather than teach
them how to use their head.

Kids are still taught basic math without a calculator, but move on the advanced subjects that require a calculator to complete...

Tell me: How do you calulate the logarithm of a number with pencil and paper? Or, a square root?

[KA5PIU]

Hello.

You can easily plot a graph with a slide rule, don't have one? create a number line in 2D and extrapolate.
Not that precise, I can only do around 2 inches of error, per mile (5280 feet). ;)
Not that bad for a bulldozer bum.
I remember when I could actually afford a real TI-58 calculator!
Prior to that I had to be content with my Electronica (Soviet) calculator!

[N7RJD]

Kids are still taught basic math without a calculator, but move on the advanced subjects that require a calculator to complete...

Tell me: How do you calulate the logarithm of a number with pencil and paper? Or, a square root?

The same way I calculate who will take a joke/shot at the public school system combination
seriously.

[W3WN]

Personally the only problem I've ever had with calc
is when the batteries died and a bad time.

Oh, you meant calculus, I though you meant people
couldn't operate calculators. I remember when the
things were damn near outlawed in school where now
they seem to teach kids to rely on them rather than teach
them how to use their head.

My daughter's school not only permits calculators, they specify a specific make & model that is to be used for homework assignments.

Little Miss Field Day is often amazed that when I help her on her homework, I can do the calculations in my head faster. And yes, I've said something to the teacher. Went in one ear and out the other.

[W3WN]

< snip >
Tell me: How do you calulate the logarithm of a number with pencil and paper? Or, a square root?

Very carefully.

[cue: rimshot]

Now, where did I put that old slide rule?

[N7RJD]

My daughter's school not only permits calculators, they specify a specific make & model that is to be used for homework assignments.

Little Miss Field Day is often amazed that when I help her on her homework, I can do the calculations in my head faster. And yes, I've said something to the teacher. Went in one ear and out the other.

When I was in school they provided a lot of the supplies (maybe why that school district went bankrupt.)
I was actually surprised to find that by the time my kids went to school they were providing lists each year
with specified supplies. Of course these lists are also provided to the local retailers including Office Max and
Office Depot for our convenience (nice to say anyway.)

They told us that each student had to come with their own supplies and there were to be no exceptions. When
questioned as to the quantity of some supplies that were obviously over the top for one student they stated
the excess would be used for students that didn't bring their own. One thing that hasn't changed is the less than
skillful way they can double talk themselves into a corner.

[N2NH]

Personally the only problem I've ever had with calc
is when the batteries died and a bad time.

Oh, you meant calculus, I though you meant people
couldn't operate calculators. I remember when the
things were damn near outlawed in school where now
they seem to teach kids to rely on them rather than teach
them how to use their head.

I forgot my calculator in my engineering math class and for a whole double period had to rely on my fingers and my head. No biggie, thanks to growing up when that was more normal than not. In many cases I was finished with the problem at the same time or before they were with calculators. Amazed the yokels, but I am sure that the calculator should never be the end all and be all.

[n2ize]

Yep. And forgetting the constant has been the difference between passing and failing an exam for more than one person.

The problem isn't necessarily calculus; the problem is really poor math instructors.

The constant is critical because when you take the indefinite antiderivative you are really defining a class of functions all of who's derivative is the integrand.. I suspect that is what most instructors are trying to get across and most likely why they make such a fuss about the constant. However, i don't think an instructor should mark the entire problem wrong just because the student forgot to add the +C. Reason I say this is because I've seen a lot of well seasoned instructors forget to write the +C. It's one of those things that is just human nature to forget to do. Especially after you just did 2-3 pages of writing to figure out the integral. At most it should cost a point or two...

Heck, I am sure Issac Newton and Gottfried Liebniz occasionally forgot to write in the +C :-D:-D

[n2ize]

I forgot my calculator in my engineering math class and for a whole double period had to rely on my fingers and my head. No biggie, thanks to growing up when that was more normal than not. In many cases I was finished with the problem at the same time or before they were with calculators. Amazed the yokels, but I am sure that the calculator should never be the end all and be all.

Most of my math classes calculators were not permitted. Of course I was not in engineering and since these were not engineering courses so most of the time a calculator would have been useless anyway.

I do remember using the slide rule occasionally both in high school and at home. And in decades gone by the slide rule was the symbol of the engineer and the scientist. I still own a slide rule and I still occasionally use it Few people these days know how to use them anymore.

[n2ize]

Kids are still taught basic math without a calculator, but move on the advanced subjects that require a calculator to complete...

In college most higher level math courses don't use calculators. Some don;t even permit them on exams. Even college level calculus they are not really needed. And in many math courses they are useless. Even in my discrete math and probability courses we were not permitted to use them.


Tell me: How do you calulate the logarithm of a number with pencil and paper? Or, a square root?

Same way that a calculator does it. You can use such simple techniques as linear or quadratic approximations, a Taylor series, or differentials. Matter of fact you can use these techniques for cube roots, 4th roots 5th roots, etc. Just pick a suitable base point. In most cases a linear approximation works well enough.

However, in high school we often used tables or a slide rule.

[KC2UGV]

Very carefully.

[cue: rimshot]

Now, where did I put that old slide rule?


In college most higher level math courses don't use calculators. Some don;t even permit them on exams. Even college level calculus they are not really needed. And in many math courses they are useless. Even in my discrete math and probability courses we were not permitted to use them.



Same way that a calculator does it. You can use such simple techniques as linear or quadratic approximations, a Taylor series, or differentials. Matter of fact you can use these techniques for cube roots, 4th roots 5th roots, etc. Just pick a suitable base point. In most cases a linear approximation works well enough.

However, in high school we often used tables or a slide rule.

Tables or slide rules...

Are those not the same thing as punching it into a calculator? They both just take longer?

As for using the methods you outlined, they are not taught until you after you need to start figuring out those, for use in equations and the like.

And, yes, most college level math courses don't permit a calculator, and there's a simple reason for that: You are not really doing complicated arithmetic, which is better suited to be done on some form of computation device. In fact, the hardest arithmetic used in college level math is addition, subtraction, and multiplication. Division is usually just left in it's notation, or it's reduced.

[n2ize]

Tables or slide rules...

Are those not the same thing as punching it into a calculator? They both just take longer?
[/

As for using the methods you outlined, they are not taught until you after you need to start figuring out those, for use in equations and the like.


The methods I described are generally not taught until calculus. But there are other methods that were once taught to kids in grammar school for finding sqrts. One was the "guess and verify" method. If your looking for the square root of y and you know it's between the square roots of x and z then you simply "guess and verify by guessing a likely value within that interval and testing by squaring to see how close you come to the original value. Not a great method but, it does work and you can come reasonably close.. A slightly more advanced method is the "long division" algorithm we used in junior high school.

In short you asked how would it be done on paper ? There are 5 different methods.




And, yes, most college level math courses don't permit a calculator, and there's a simple reason for that: You are not really doing complicated arithmetic, which is better suited to be done on some form of computation device. In fact, the hardest arithmetic used in college level math is addition, subtraction, and multiplication. Division is usually just left in it's notation, or it's reduced.

Higher math you are more interested in where a formula comes from or why it works as opposed to plugging numbers in and cranking out answers. Thats why engineers and finance students use calculators and math students don't. Also, calculators are relatively useless in advanced proof oriented courses. Graphing calculators are a bit more useful especially for analytic geometry and of course computers are quite useful.

[W1GUH]

"This thread is brought to you by the number e."

Ripped off from the Simpson's last night! (It was also brought to us by the letter "Gamma" (I think))

[W7XF]

Slide rules were in the process of being phased out by calculators when I was in high school. My algebra teacher did show us some basics on a slide rule, on one of the few days when he was not rip-roaring drunk in class. Although, I managed a 'C' in HS algebra without electronic assistance. Not bad for a kid with Aspergers.

[NQ6U]

I learned how to do multiplication and division on a slide rule when I was in the eighth grade. I doubt that I'd remember how any more, but I do recall when you could buy a cheap plastic slide rule at the drugstore for a couple of bucks.

[n2ize]

The toughest part of any of these tests is brain fatigue. Even if the test is relatively easy, after reasoning and solving 6-7 problems in a row you need a break, but you can't take a break or you'll run out of time for the exam. So you wind up hitting that challenging problem at the end of the test and you get stuck and time is running out and you can;t seem to be able to work it out. So you end up handing in the paper with the last problem not finished. About an hour after the exam is over you think about the problem and have no problem reasoning it out. Problem is that when you run your brain in high gear for too long you need a break. After the break everything kicks back in again.