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.

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?

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 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.

this is not worth having a disagreement about. i do not disagree with butler. more later, perhaps.

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.

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.

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.