To JM
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To JM
Single variable calculus
The idea behind calculus is to study things which
are not flat by things which are flat. For example,
curves will look like lines when we zoom in close and
areas can be broke into strips that look like rectan-
gles; since we know about lines and rectangles then
we can say something about the curves and the area.
The underlying idea behind this are limits which tell
us what should happen based on what is happening
nearby.
I have copied and pasted what professor Steve Butler had mentioned in his course syllabus. He now works at Iowa State University.
Do you agree with this or not?
If you don't agree with this description of what calculus is about, please explain why.
Thanks.
The idea behind calculus is to study things which
are not flat by things which are flat. For example,
curves will look like lines when we zoom in close and
areas can be broke into strips that look like rectan-
gles; since we know about lines and rectangles then
we can say something about the curves and the area.
The underlying idea behind this are limits which tell
us what should happen based on what is happening
nearby.
I have copied and pasted what professor Steve Butler had mentioned in his course syllabus. He now works at Iowa State University.
Do you agree with this or not?
If you don't agree with this description of what calculus is about, please explain why.
Thanks.
Rishi- Posts : 5129
Join date : 2011-09-02
Re: To JM
Rishi wrote:Single variable calculus
The idea behind calculus is to study things which
are not flat by things which are flat. For example,
curves will look like lines when we zoom in close and
areas can be broke into strips that look like rectan-
gles; since we know about lines and rectangles then
we can say something about the curves and the area.
The underlying idea behind this are limits which tell
us what should happen based on what is happening
nearby.
I have copied and pasted what professor Steve Butler had mentioned in his course syllabus. He now works at Iowa State University.
Do you agree with this or not?
If you don't agree with this description of what calculus is about, please explain why.
Thanks.
you have now taken a course in single variable calculus. what do you think? do you agree with this description?
MaxEntropy_Man- Posts : 14702
Join date : 2011-04-28
Re: To JM
MaxEntropy_Man wrote:Rishi wrote:Single variable calculus
The idea behind calculus is to study things which
are not flat by things which are flat. For example,
curves will look like lines when we zoom in close and
areas can be broke into strips that look like rectan-
gles; since we know about lines and rectangles then
we can say something about the curves and the area.
The underlying idea behind this are limits which tell
us what should happen based on what is happening
nearby.
I have copied and pasted what professor Steve Butler had mentioned in his course syllabus. He now works at Iowa State University.
Do you agree with this or not?
If you don't agree with this description of what calculus is about, please explain why.
Thanks.
you have now taken a course in single variable calculus. what do you think? do you agree with this description?
I agree with this 100%.
Rishi- Posts : 5129
Join date : 2011-09-02
Re: To JM
Sometime back when I referred to JM about what this professor said in the video, he did not agree. That is why I posted in complete what the professor had written in the syllabus.
Rishi- Posts : 5129
Join date : 2011-09-02
Re: To JM
this is not worth having a disagreement about. i do not disagree with butler. more later, perhaps.Rishi wrote:Single variable calculus
The idea behind calculus is to study things which
are not flat by things which are flat. For example,
curves will look like lines when we zoom in close and
areas can be broke into strips that look like rectan-
gles; since we know about lines and rectangles then
we can say something about the curves and the area.
The underlying idea behind this are limits which tell
us what should happen based on what is happening
nearby.
I have copied and pasted what professor Steve Butler had mentioned in his course syllabus. He now works at Iowa State University.
Do you agree with this or not?
If you don't agree with this description of what calculus is about, please explain why.
Thanks.
Jeremiah Mburuburu- Posts : 1251
Join date : 2011-09-09
Re: To JM
however, his course description is deficient because it does not mention continuous change, which is the subject that calculus addresses, whose study is the reason for its existence. "study[ing] things which are not flat by things which are flat" or a mention of limits is inadequate.Jeremiah Mburuburu wrote:this is not worth having a disagreement about. i do not disagree with butler. more later, perhaps.Rishi wrote:Single variable calculus
The idea behind calculus is to study things which
are not flat by things which are flat. For example,
curves will look like lines when we zoom in close and
areas can be broke into strips that look like rectan-
gles; since we know about lines and rectangles then
we can say something about the curves and the area.
The underlying idea behind this are limits which tell
us what should happen based on what is happening
nearby.
I have copied and pasted what professor Steve Butler had mentioned in his course syllabus. He now works at Iowa State University.
Do you agree with this or not?
If you don't agree with this description of what calculus is about, please explain why.
Thanks.
Jeremiah Mburuburu- Posts : 1251
Join date : 2011-09-09
Re: To JM
Jeremiah Mburuburu wrote:however, his course description is deficient because it does not mention continuous change, which is the subject that calculus addresses, whose study is the reason for its existence. "study[ing] things which are not flat by things which are flat" or a mention of limits is inadequate.
that is why isaac newton referred to calculus as the method fluxions which is very apt. amongst the many meanings of flux is change.
MaxEntropy_Man- Posts : 14702
Join date : 2011-04-28
Re: To JM
yes. i had his principia in english somewhere. i must find it again.MaxEntropy_Man wrote:Jeremiah Mburuburu wrote:however, his course description is deficient because it does not mention continuous change, which is the subject that calculus addresses, whose study is the reason for its existence. "study[ing] things which are not flat by things which are flat" or a mention of limits is inadequate.
that is why isaac newton referred to calculus as the method fluxions which is very apt. amongst the many meanings of flux is change.
Jeremiah Mburuburu- Posts : 1251
Join date : 2011-09-09
Re: To JM
I guess the professor was referring to the Riemann sum formula for finding definite integral using rectangles.
I agree that he should have talked about infinitesimal changes. I wonder why he did not mention that also. He has a Ph.D in mathematics from UCLA.
I agree that he should have talked about infinitesimal changes. I wonder why he did not mention that also. He has a Ph.D in mathematics from UCLA.
Rishi- Posts : 5129
Join date : 2011-09-02
Re: To JM
i'm sure he's well-qualified to teach the course.Rishi wrote:I guess the professor was referring to the Riemann sum formula for finding definite integral using rectangles.
I agree that he should have talked about infinitesimal changes. I wonder why he did not mention that also. He has a Ph.D in mathematics from UCLA.
Jeremiah Mburuburu- Posts : 1251
Join date : 2011-09-09
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