Calc 1 topics to prepare for Calc 2

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Discussion Overview

The discussion revolves around preparation for Calculus 2, focusing on the foundational concepts and skills from Calculus 1 that are deemed important for success in the subsequent course. Participants share their experiences, challenges, and tips related to various calculus topics, particularly application problems, derivatives, and integration techniques.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant expresses concern about understanding math language and seeks tips for better comprehension as they prepare for Calculus 2.
  • Another participant emphasizes the importance of mastering derivative rules, particularly the product rule, quotient rule, and chain rule, as these are foundational for integration.
  • Discussion includes the significance of being proficient in sketching graphs for applications involving definite integrals.
  • A participant mentions their proficiency with derivatives but struggles with applying concepts to real-world problems, particularly in optimization scenarios.
  • Specific examples of application problems causing difficulty include related rates and optimization problems related to geometric shapes.
  • One participant highlights that Calculus 2 will involve integrals, derivatives, series, and sequences, suggesting a focus on these areas for preparation.

Areas of Agreement / Disagreement

Participants generally agree on the importance of certain calculus concepts and skills for success in Calculus 2, but there is no consensus on specific strategies or solutions to the challenges faced in application problems.

Contextual Notes

Participants express varying levels of confidence in their understanding of calculus concepts, with some indicating proficiency while others highlight specific areas of difficulty. There is an acknowledgment of the need for practice and application of concepts in different contexts.

Who May Find This Useful

Students preparing to transition from Calculus 1 to Calculus 2, particularly those seeking to improve their understanding of application problems and integration techniques.

Slimjimjohnso
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I am taking calculus 1 right now and we have been doing a lot of application problems. Like related rates and finding and relating maximum values. I don't have any specific question I was just wanting to maybe have an open forum where we could discuss tips in understanding math->language a little better. I would really appreciate any little nuggets are suggestions any of you guys have.

I will be going on to calc 2 this fall and I am sort of nervous because this class is somewhat challenging for me and all my friends who are in calc 3 or higher keep saying it is easy. I don't find it all that easy. Is there anything I should really really pay attention to in order to be prepared for calc 2?
 
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What is calc 1?
 
alice22 said:
What is calc 1?
Very likely it's the first quarter or semester of calculus.

Some tips...
Make sure that you are very proficient at using the product rule, quotient rule, and especially the chain rule. What you'll be doing a lot of in the second calculus course is integration, which can be thought of as backwards differentiation. If you are weak with derivatives it will come back to haunt you when you start working with antiderivatives.

You'll be exposed to several different techniques of integration: substitution, which is where the chain rule comes in; integration by parts, which is where the product rule comes in; trig substitution, which requires a good understanding of right-triangle trig.

Being able to sketch graphs of functions is important when you come to applications involving definite integrals, such as finding the area beneath a curve, volumes of solids, and others.

That's all that come to mind right now. I'm sure I've left some things out, but if you are competent at what I've listed, that should get you through maybe 75% of the things covered. A lot of the concepts of calculus are relatively simple, but where many students fall down is not being able to carry longer calculations all the way through, due to poor understanding of algebra or trig, or previous calculus classes.
 
Last edited:
It is in fact first semester calculus.

I have all of the derivative rules down pat and have become rather proficient with them. Trig isn't too big of a deal either, I mainly have problem with trig when it comes to recognizing when I can use an identity.

We started antiderivatives yesterday :)

I have a test Monday and it covers a lot of application problems. This is where most of my worry falls in, I don't have trouble understanding math concepts and going through obvious needed motions to get a result. I have trouble applying what I know to actual situations.
 
Can you give some examples of the types of applied problems that have given you difficulties? Not the specific problems, just the general types.
 
Well I was having trouble with different related rate problems, but I am not too shabby with them now. (lots of practice problems lol)

But now its optimization problems. Finding minimum of materials used in a box' construction with just the volume given. Finding the formula for the maximum sized cylinder one can fit in a sphere with radius r. Stuff like that.
 
Take it from someone who took calc 2 at the nations' #1 engineering, math and science college. Calc 2 is full of integrals (finding areas, volumes), derivatives, series' (Taylor, Maclaurin), and sequences. Focus on those 4 things and you're sure to do well.
 
(to the poster above) MIT? Cal Tech?
 
Rose-Hulman Institute of Technology
 

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