Calculus III: A Disappointing Start?

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Discussion Overview

The discussion revolves around experiences and expectations regarding Calculus III courses at different educational institutions. Participants share their thoughts on course content, difficulty levels, and the focus on visualization versus advanced calculus topics.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant expresses disappointment with the perceived ease of their Calculus III course, noting minimal coverage of calculus topics and a focus on visualizing three-dimensional space.
  • Another participant suggests that the difficulty of Calculus III varies significantly depending on the institution, with community colleges often offering a less rigorous curriculum compared to universities with strong science programs.
  • A participant mentions that their university's Calculus III course focuses on series calculus and vector functions but does not cover multiple integrals, which they believe are essential for understanding vector calculus.
  • Some participants discuss the importance of multiple integrals in Calculus III, with one noting that the process is simpler than previous topics in Calculus II.
  • There is a conversation about the challenges of setting up triple integrals in spherical and cylindrical coordinates, with differing opinions on their complexity compared to polar or Cartesian coordinates.
  • One participant suggests that the course could be better named "Understanding Mathematics in 3 Dimensions," indicating a focus on conceptual understanding rather than rigorous calculus.
  • A suggestion is made to seek out an honors section of the course for a more challenging experience.

Areas of Agreement / Disagreement

Participants express a range of opinions about the difficulty and content of Calculus III courses, with no consensus on what constitutes a standard or adequate curriculum. Some believe the course is too easy, while others acknowledge variability based on the institution.

Contextual Notes

Participants highlight differences in course structure based on institutional type (community college vs. university) and academic focus (math majors vs. non-science majors). There are also references to different academic calendars (quarter vs. semester) affecting course content.

Gale
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Hey, i just started calculus III at a local college and its a bit... weak. I know we're not going to jump right in and start doing calc with numerous variables, but it still seemed like it was going to be too easy. The review we did was pathetic. We did one differential equation and one integral. Then matched some terms. Worst was that a lot of the class did pretty poorly. I was expecting to be pretty far behind because I've only taken one AP calc class, bc level. But i really doubt that now. My professor said we'll mostly be working on being able to visualize 3 dimensions and how to graph functions in 3d. He said we likely won't do much calc at all until the very end of the course. I'm just curious, but it that regular? He said we mightn't do everything in the book, because that's for egineers and stuff, but i wonder if i should maybe just do the extra stuff on my own anyways then. I'm just wondering if the course is too easy and what other mosre challenging schools (which i hope to get in to) will be like.

~abigale~
 
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Calc III can be very difficult and easy. The difference lies in where you take the class.

If your're taking the couse at a community college then, the course is geared towards non science majors. The empahsis is geared toward basic calculation of vectors and the like.

If your'e taking the course at a school like Georgia Tech (I live in Atl.) or Georgia State Univ. (kickass physics dept.) then the course is going to deal with vector operators (div grad, curl), Stokes Theorem and so on. For Math majors the course is going to stress proofs and contain more Linear Algerbra.

I'm a physics major who wound up taking the couse at a community college. It sucked. We didn't even cover mutiple integrals. It was a essientially Cal II review with vectors. I would have been eaten alive in EMAG or Mechanics. I had to cover most of the advanced material myself. :mad:

I recommend this book:

div, grad, curl and all that: an informal text on vector calculus
by H.M. Schey
 
At the Univ. of Washington we are on a quarter system, and our Calculus III course is actually geared toward Series Calculus (Including Taylor) and Vector functions with an introduction to multivariable differential calculus. We did not however, go into Multiple Integrals, and thus did not go into Vector calc at all, since you must really understand Multiple Integrals to understand the important theorems in v.analysis.

So it depends on whether your college is quarter, semester or trimester. I found Calc II (integral) harder than calc III at my school.
 
Calc 3 is the most fun of the 3. you learn very few new things but rather you learn how to apply all the stuff you have learned... and vectors are the best part I think.
 
no multiple integrals? but those are one of the best things in calc 3, especially when you realize that the process is simpler than finding the volume of revolutions in cacl 2.
 
True but when setting up triple integrals of dV using spherical and cylindrical coordinates? It gets pretty tedious :(
 
naw... Spherical and cylindrical coordinates are not that much harder than polar or cartesian. you just have to remember more stuff.
 
well ya, the school I'm going to is a liberal arts school, sort of community college. There are math majors in the course, i don't know how they feel about it. It seems we'll be mostly learning about how to visualize 3d space. Maybe a little calc... I don't know about vectors or second intergrals... all i know is he's even said the course would be more aptly named "Understanding mathematics in 3 dimensions" or something like that. I dunno. It seems easy, which i don't mind i decided. He said our book is versatile and used in engineering schools, but that we won't go over most of it. So i can always do extra work on my own, which is ok, cause i have all you's to help me out! :biggrin:
 
get out of that cruddy class and into the honors section. you are paying money for this. talk to the chairman of the department aboiut your concerns. they love to find good students and help them get placed correctly.
 

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