Calculus 4 Has Another Name

mathdad

mathdad

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I've heard many tutors, teachers and college professors say that Ordinary Differential Equations is just another name for Calculus 4. Is this true? If it is true, what makes this statement true? Let me guess: Advanced Integration?
 
What's in a name? A rose by any other name would smell as sweet.
 
mathdad said:
I've heard many tutors, teachers and college professors say that Ordinary Differential Equations is just another name for Calculus 4. Is this true?
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Are these people all at the same school? Different schools/authors may assign different names for essentially the same thing, so I don't think your question has a definitive answer.

The name 'Calculus 4' doesn't really have any meaning, for me. What is it?

?
 
mathdad said:
I've heard many tutors, teachers and college professors say that Ordinary Differential Equations is just another name for Calculus 4. Is this true? If it is true, what makes this statement true? Let me guess: Advanced Integration?
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Actually I have never seen the title Calculus IV used. As well I have never see Differential Equations named anything else. Often Calculus III is named Multivariable Calculus. There is a great text book by that name by Smith&Minton. That is a wonderful text for undergraduate Vector Analysis
When calculus courses became five semester hour credit courses, it became necessary to add content to Cal III. We do have course called Advanced Caculus which is a basic introduction to analysis for mathematics majors who plan to attend graduate school.
 
pka said:
Actually I have never seen the title Calculus IV used. As well I have never see Differential Equations named anything else. Often Calculus III is named Multivariable Calculus. There is a great text book by that name by Smith&Minton. That is a wonderful text for undergraduate Vector Analysis
When calculus courses became five semester hour credit courses, it became necessary to add content to Cal III. We do have course called Advanced Caculus which is a basic introduction to analysis for mathematics majors who plan to attend graduate school.
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How hard is Advanced Calculus?
 
mathdad said:
How hard is Advanced Calculus?
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You need to fully understand that most so called Advance Calculus courses could be named the theory of calculus.
The difficulty the depends upon how well a student is prepared in proofs and the theory of limits.
I say without fear of contradiction, Advanced Calculus is most like graduate mathematics courses as are any undergraduate mathematics course.
 
I too have never heard or ever seen written that differential equations and calculus IV are the same. For the record I have never heard of calculus IV either.
Having said that I need to say why someone may say this. When I took differential equations I felt that it was a simply a continuation of calculus 2 (integral calculus). The rate of difficulty was the same as calculus 2 and it was basically more techniques of integration (asin a calculus 2 course).
 
Jomo said:
I too have never heard or ever seen written that differential equations and calculus IV are the same. For the record I have never heard of calculus IV either.
Having said that I need to say why someone may say this. When I took differential equations I felt that it was a simply a continuation of calculus 2 (integral calculus). The rate of difficulty was the same as calculus 2 and it was basically more techniques of integration (asin a calculus 2 course).
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I guess differential equations involve lots of integration, which is the reason why it is called calculus 4 by some people on youtube. Honestly, calculus 1, 2, and 3 should be taught one year per course instead of one course per semester. I think students would benefit more from calculus material if they are not bombarded with tons of information per semester not to mention additional courses they must take at the same time.

My Idea For Calculus Divided:

Calculus 1 Part A
Calculus 1 Part B
Together = 1 year

Calculus 2 Part A
Calculus 2 Part B
Together = 1 year

Calculus 3 Part A
Calculus 3 Part B
Together = 1 year

Each part represents a semester. What do you say?
 
I understand your point but then you will only one year left to take advanced math courses (if you are a math major) which is not enough time to take a dozen math courses.
 
mathdad said:
My Idea For Calculus Divided:
Calculus 1 Part A
Calculus 1 Part B
Together = 1 year
Calculus 2 Part A
Calculus 2 Part B
Together = 1 year
Calculus 3 Part A
Calculus 3 Part B
Together = 1 year
Each part represents a semester. What do you say?
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I say that it is completely obvious that this is not a proposal for a secondary school.
AP Calculus is so well defined, any changes will have to be made by the testing company.
Thus I assume this is a proposal for college calculus courses. If so I can only say that it is clear that you have never had to deal with any regional accreditation teams. Two semesters of five hours each is a standard for the calculus sequence. Thus the standard is a one year course. Under your proposal above a mathematics major would be a six or seven year college course. Colleges must assume that students come to us reasonably prepared to succeed. We attempt to offer courses to meet all needs.
 
pka said:
I say that it is completely obvious that this is not a proposal for a secondary school.
AP Calculus is so well defined, any changes will have to be made by the testing company.
Thus I assume this is a proposal for college calculus courses. If so I can only say that it is clear that you have never had to deal with any regional accreditation teams. Two semesters of five hours each is a standard for the calculus sequence. Thus the standard is a one year course. Under your proposal above a mathematics major would be a six or seven year college course. Colleges must assume that students come to us reasonably prepared to succeed. We attempt to offer courses to meet all needs.
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The fact remains that most students walk into college without proper preparation, especial for calculus. I never took calculus formally but I did take precalculus in the Spring 1993 semester at Lehman College as an elective. I got an A minus but of course this was 26 years ago. Boy, I'm getting old.
 
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