Transition from AP Calc BC to Multivariable Calc

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Discussion Overview

The discussion centers around the transition from AP Calculus BC to Multivariable Calculus in college. Participants explore the adequacy of AP Calculus BC preparation for college-level Multivariable Calculus, considering topics covered in both courses and the potential need for additional review or coursework.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant expresses concern about gaps in their AP Calculus BC education, particularly regarding integration techniques not covered by their teacher.
  • Several participants inquire about specific integration methods, such as substitution, partial fractions, and improper integrals, suggesting these may be important for success in Multivariable Calculus.
  • Some participants argue that Multivariable Calculus is more similar to Calculus I than Calculus II, indicating that the integration techniques from Calculus II may not be as relevant.
  • One participant shares their experience of successfully transitioning to Multivariable Calculus without taking Calculus II, suggesting confidence in their preparation.
  • Another participant mentions that a solid foundation in linear algebra may be more beneficial for Multivariable Calculus than mastery of integration techniques.
  • Concerns are raised about the necessity of certain integration techniques, with some arguing that they may not be frequently used in Multivariable Calculus.
  • There is a discussion about the relevance of hyperbolic trigonometric functions, with some participants noting they are not covered in AP Calculus BC.

Areas of Agreement / Disagreement

Participants express a mix of opinions regarding the necessity of taking Calculus II before Multivariable Calculus. While some advocate for taking Calculus II to reinforce integration techniques, others believe that a strong foundation in single-variable calculus is sufficient for success in Multivariable Calculus. The discussion remains unresolved regarding the best preparatory path.

Contextual Notes

Participants highlight various topics and techniques that may or may not be covered in their respective courses, indicating a lack of consensus on what is essential for Multivariable Calculus. There are also differing views on the importance of linear algebra in relation to calculus topics.

battousai
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Hello everyone, I'm new to this forums. Been lurking around for a while, but finally decided to join :)

So anyways, I'm a current high school senior right now, taking Calc BC. I'm hoping to major in a math-related field (mathematics, physics, or electrical engineering) when I get to college. Consequently I'm looking to transfer my credits from Calc BC (I'm fairly certain I can get a 5 on the test) so that I'll be taking Multivariable Calc freshman year in college.

However, here is where my dilemma lies. Looking at a typical Calc 2 syllabus, I see some topics not covered in my BC class, mostly dealing with further integration techniques. Also my teacher is the "minimalist" type of guy, he just teaches the bare essentials to score well on the AP test and skipping over the ones he feels that "is not going to be on the test".

My question I guess would be if transfering my BC credit would be a smart choice, or should I take Calculus 2 again in college?
 
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Have you practiced subs, trig subs, parts, partial fraction decomposition as methods of integration? Are you familiar with improper integrals? What have you learned about convergence/divergence or series? Can you form a Taylor / Mclaurin series?

If so you should be good.
 
Knowing how to find the volume of a solid of revolution is always good too. If you can do Work problems, then that is also a plus.
 
JonF said:
Have you practiced subs, trig subs, parts, partial fraction decomposition as methods of integration? Are you familiar with improper integrals? What have you learned about convergence/divergence or series? Can you form a Taylor / Mclaurin series?

If so you should be good.

I don't think trig subs and integration by partial fractions are part of the curriculum. The hardest integration problems on the test are integration by parts. Improper integrals, Taylor and Maclaurin series are covered.

However, my friend said that calculus 2 in college is harder than calculus BC. That's another aspect that scares me. Maybe if I jump straight to calc 3 I might be overwhelmed by the difficulty of tests.


Has anyone here transitioned smoothly from Calc BC to Multivariable in college?
 
I’ve tutored a good deal of Calc BC and Calc 3. I’d learn those topics I mentioned before you attempt calc3.
 
Is Calc 3 like Calc 2 in that it's filled with all the nasty integrals?
 
No, Calc III is much more similar to Calc I than Calc II - there is just more variables. There are no series to worry about and most integration is simple.
 
RIyzar said:
No, Calc III is much more similar to Calc I than Calc II - there is just more variables. There are no series to worry about and most integration is simple.

So would I still need to go over the integration techniques (partial fractions, trig subs) that are not going to be covered?
 
I am actually doing multivariable calc right now as a freshman, and i can assure you, you will be fine. (As long as you put the work in obviously)
 
  • #10
I was in the same position as you last year (and asking the exact same question). Trust me, don't take Calc II in college. You'll be fine.
 
  • #11
You rarely ever use trig substitution and partial fraction integ. in multivar. As long as you have a solid foundation in single-variable calculus you'll be fine.
 
  • #12
Personally, I feel that since the advent of the TI-89 calculator, integration techniques by hand has been rendered obsolete. lol

Seriously, get one of those things even if you take Calculus 2 again. And taking it is your own choice. If you're dedicated, you could always just go over integration techniques on your own or just audit a class.

good luck
 
  • #13
royzizzle said:
Personally, I feel that since the advent of the TI-89 calculator, integration techniques by hand has been rendered obsolete. lol

Yeah, but I don't think educators/we want integration to become a 'black box'.
 
  • #14
General_Sax said:
Yeah, but I don't think educators/we want integration to become a 'black box'.

I wasn't completely serious lol.

I'm just commenting on how learning integration techniques may not be a totally necessary thing anymore
 
  • #15
What about hyperbolic trig functions? We don't cover that in Calc BC.
 
  • #16
I wouldn't worry about the calculus aspect of calc 3, having a solid base in linear algebra will do you much more good in a multivariable course than any memorized identity or procedure related to calc 1 or 2
 
  • #17
So I should take L.A. first?
 
  • #18
I'm not sure why you would need all those different methods of integration and Taylor expansion stuff for Multivariable Calculus. That stuff is useful for its purposes but not knowing it I think you'd be fine. If need be you can probably brush up on those topics sufficently pretty quick. Most the time in Multivariable Calc you'll have a pretty simple integrand the work will come in defining the region you are integrating over and other techniques.

Most important to know for that class I think is:

Basic Linear Algebra
Understanding of Polar Coordinates
Differentiation and Basic Integration(Up to Integration By Parts)
Parametric Equations

If your professor gives you on a Calc 3 test an integral that has to be solved by some crazy and lengthy method they are just being mean.
 
Last edited:
  • #19
battousai said:
So I should take L.A. first?

Do you understand a few basics about linear algebra and in particular the 3D vector and scalar spaces? I took it w/o LA and got an A. Most of the time the first 1/4th of the class or so is dedicated to teaching enough LA to get you up to speed. You could probably take both at the same time and see that they complement each other very well.
 
  • #20
Also do note that you will probably need to at least know how to break up a rational polynomial into partial fractions, something that is sometimes taught in "Calc II" for Differential Equations. But again if you are taking AP Calc and getting top scores I think you won't have much trouble learning that stuff pretty quickly once you need to.
 
  • #21
battousai said:
What about hyperbolic trig functions? We don't cover that in Calc BC.

You would have to pretty specialized to ever see these again in any class you take after Calc II they will almost certainly not show up in Calc III.
 

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