Calculus I review for Calculus II

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Discussion Overview

The discussion centers around the preparation needed for Calculus II after a significant gap since taking Calculus I. Participants explore key concepts that should be reviewed, including derivatives, limits, and trigonometric identities, as well as the differences between the calculus courses.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants emphasize the importance of reviewing derivatives and limits as foundational concepts for Calculus II.
  • Trigonometric derivatives and identities are also highlighted as essential knowledge.
  • There is a mention of variability in curriculum, with some participants noting that L'Hôpital's rule may be taught in different courses depending on the institution.
  • One participant suggests that having a strong basis in integration is crucial for success in Calculus II, which focuses on more advanced integration techniques.
  • Another participant points out that differentiation is not significantly harder if L'Hôpital's rule has already been learned, although this claim is challenged by another who states that L'Hôpital's rule is primarily for limits, not differentiation.
  • Several participants recommend reviewing a textbook and practicing problems to reinforce understanding of the major concepts.
  • There are suggestions to utilize online resources, such as tutorial websites and YouTube videos, for additional support.

Areas of Agreement / Disagreement

Participants generally agree on the importance of reviewing derivatives, limits, and trigonometric identities. However, there are differing opinions on the specifics of what is essential for preparation and the role of L'Hôpital's rule, indicating that the discussion remains somewhat unresolved.

Contextual Notes

There are limitations regarding the assumptions about what constitutes essential knowledge for Calculus II, as well as the dependence on individual school curricula. The discussion does not resolve the differences in opinions on the importance of various concepts.

Kryptnick
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I'm scheduled to take Calculus II this Fall semester, but it will have been over a year since I'd taken Calculus I. I am aware that I need to review, but what are some are the major concepts I should review to adequately prepare for the infamous Calc II?
 
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Derivatives and limits, so the two biggies. Also make sure you're well versed in trig. I.E. Trig derivatives and identities.

It should be noted that it varies from school to school, L'Hospital's rule for example, I learned that in Cal I at one school, ad then again in Cal II at another school.
 
Ok thanks, Yea I learned L'Hospital's rule in Calc I. I have a whole textbook for review but just want to review only the major concepts. So I'll get the hang of those derivatives and limits again.
 
If you've got the textbook, I'd just go through and see what concepts you do remember and which you don't.
 
I would say that Calculus II is fairly different from both Calculus I and III (which I felt were similar). Having a strong basis in integration is good for Calc. II though, you'll learn more advanced methods of integration. If I remember correctly, differentiation isn't all that much harder if you've already learned L'Hôpital's.

To be honest, Calculus II was a lot of summation, which I haven't really used that much (EE, so I've been using a lot of the information from Calculus III).
 
Gleveniel said:
I would say that Calculus II is fairly different from both Calculus I and III (which I felt were similar). Having a strong basis in integration is good for Calc. II though, you'll learn more advanced methods of integration.
In many calculus sequences, the first course deals with differentiation, the second course with integration, and the third with infinite series and things like line and surface integrals. The most important thing before learning the integration part is having a solid understanding of differentiation.
Gleveniel said:
If I remember correctly, differentiation isn't all that much harder if you've already learned L'Hôpital's.
That last sentence doesn't make much sense. You can't use L'Hopital's Rule without already knowing how to differentiate. In any case, L'Hopital's Rule is used primarily for limits, not for differentiating functions.
Gleveniel said:
To be honest, Calculus II was a lot of summation, which I haven't really used that much (EE, so I've been using a lot of the information from Calculus III).
 
Jesse H. said:
Derivatives and limits, so the two biggies. Also make sure you're well versed in trig. I.E. Trig derivatives and identities.

It should be noted that it varies from school to school, L'Hospital's rule for example, I learned that in Cal I at one school, ad then again in Cal II at another school.

I second these. It's not how you perform the derivatives etc. It's the definitions, the very basics. Like what is a derivative, the definition of limits, Rollies, L'Hospital's, Mean value...All the basics.
 
Jesse H. said:
Derivatives and limits, so the two biggies. Also make sure you're well versed in trig. I.E. Trig derivatives and identities.

It should be noted that it varies from school to school, L'Hospital's rule for example, I learned that in Cal I at one school, ad then again in Cal II at another school.

Pretty much this. It does vary school to school, but at least brush up some on trig.

Brown Arrow said:
you should check out http://tutorial.math.lamar.edu/ <--- Its Pauls notes on Calculus I II III it got examples so it should be good.

I just skimmed through this, but it looks pretty decent, so I'd give it a go. You could also look up YouTube videos.

yungman said:
I second these. It's not how you perform the derivatives etc. It's the definitions, the very basics. Like what is a derivative, the definition of limits, Rollies, L'Hospital's, Mean value...All the basics.

Yes, maybe even perhaps grab a textbook and look through it while doing some practice problems.

Goodluck!
 

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