Is Calculus Just an Extension of Pre-Calculus?

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Discussion Overview

The discussion centers on the relationship between Pre-Calculus and Calculus, exploring whether Calculus is simply an extension of Pre-Calculus or if it introduces significantly different concepts. Participants share their experiences with both subjects, discussing the content and difficulty of Calculus compared to Pre-Calculus.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • Some participants express confusion about the term "Pre-Calculus with derivatives," suggesting it may overlap with introductory Calculus concepts.
  • There is mention of the importance of algebra skills for success in Calculus, with some arguing that Pre-Calculus typically emphasizes algebra more than Calculus.
  • One participant outlines typical topics covered in a first Calculus course, including limits, derivatives, and integrals.
  • Another participant describes a course structure that integrates Pre-Calculus and Calculus content, suggesting a blended approach to learning these subjects.
  • Some participants question the difficulty of Calculus compared to Pre-Calculus, with varying opinions on whether Calculus is harder or easier.
  • There are anecdotal accounts of students struggling with Calculus after taking Pre-Calculus, with suggestions that Pre-Calculus may not adequately prepare them for Calculus concepts.
  • Several participants seek resources for learning Calculus, indicating a desire for additional support in understanding the subject.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether Calculus is simply an extension of Pre-Calculus or if it introduces fundamentally different concepts. There are multiple competing views regarding the difficulty and content overlap between the two subjects.

Contextual Notes

Some participants note that the curriculum and teaching methods for Pre-Calculus and Calculus can vary significantly, which may influence their perspectives on the relationship between the two subjects.

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I've studied Pre-Calculas with derivitaves and all but not Calculas. Is it that much different from Precal or is it about the same as Precal?
 
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I'm not sure what you mean by "Pre-Calculus with derivatives". That sounds like at least the first part of Calclulus! You do need to be very, very good at algebra in order to do calculus so "pre-calculus" typically involves a lot of algebra. How much like or unlike calculus it is depends a lot on the particular course. Some of the concepts in calculus, particularly those involving limits, are very subtle and very different from "before calculus" courses.
 
Just what does a typical Calculas course consist of?
 
Line said:
Just what does a typical Calculas course consist of?

  • Limits and Rates of Change
    Derivatives
    Applications of Derivatives
    Antiderivatives,Integrals, Definite Integrals, indefinite integrals
    Applications of Integration

Thats a typical of topics for calculus 1.
 
Last edited:
HallsofIvy said:
I'm not sure what you mean by "Pre-Calculus with derivatives". That sounds like at least the first part of Calclulus! You do need to be very, very good at algebra in order to do calculus so "pre-calculus" typically involves a lot of algebra. How much like or unlike calculus it is depends a lot on the particular course. Some of the concepts in calculus, particularly those involving limits, are very subtle and very different from "before calculus" courses.
In my precalculus class a while back I studied derivatives at the very end of the course. However, most of single-var. differential calculus was actually taught in calc. 1. Is this similar to what you're thinking of?

Alex
 
Where I teach we have a sequence entitled "Calculus with Precalculus I-II". I don't know how common it is, but basically it has all the material from Precalculus and Calculus I folded in together. The idea is that you learn a that bit of Precalc that you need for a particular Calc unit, right before you need it.

Maybe that's what the OP is getting at.
 
I got Precal but is Calculas much harder?
 
Line said:
I got Precal but is Calculas much harder?

You won't know until you try it :P
But I think most people would agree that of all the "post-precal" mathematics, calculus would be the easiest, even in vector form.
 
I know a lot of kids who took precalc , which isn't really all that worthwhile IMAO ,... i didn't do it, I just went to calc ... and the kids struggled a little, but it was only because the stuff was new to them .. like precalculus didn't really give them skills to be used in calculus.. then again they also didn't cover the state standards and stuff, so maybe i was better off ...
 
  • #10
I need a website that explains Calculus.
 
  • #11
Here is a good website on calulus 1 and 2 topics. http://archives.math.utk.edu/visual.calculus/

Here is one for calc 3 stuff
http://tutorial.math.lamar.edu/AllBrowsers/2415/2415.asp
 
Last edited by a moderator:
  • #12
Line said:
I've studied Pre-Calculas with derivitaves and all but not Calculas. Is it that much different from Precal or is it about the same as Precal?

Upon the schedual of the pre-cal classes, most teacher would introduce the definition of derivative by using limit. Moreover, I assume that they will not go into power rule and anything beyond.
 

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