Multivariate and vector calculus

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Discussion Overview

The discussion revolves around the prerequisites and foundational knowledge beneficial for a course in multivariate and vector calculus. Participants share their experiences and suggest topics to review, focusing on the interplay between calculus and linear algebra.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant suggests that prior knowledge in single variable calculus and vectors is essential.
  • Another participant advocates for taking multivariate and vector calculus alongside linear algebra.
  • A participant currently enrolled in a multivariable and vectors course emphasizes the importance of integration, noting that half of their course has focused on it.
  • One contributor mentions specific topics to review, including parametric equations, arc length, coordinate systems, integration techniques, and vector operations such as dot products and cross products.
  • Another participant points out that different textbooks may present the material in varying orders, with some starting with vectors before moving to multivariable concepts.

Areas of Agreement / Disagreement

Participants generally agree on the importance of prior knowledge in calculus and vectors, but there are differing opinions on the sequence in which topics should be taught and the emphasis on integration techniques.

Contextual Notes

Some participants express uncertainty about the specific order of topics in their courses and the extent to which linear algebra is integrated with calculus concepts.

Who May Find This Useful

Students preparing for courses in multivariate and vector calculus, as well as those interested in the relationship between calculus and linear algebra.

dynamics
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Hi everyone I'm just about to begin a course in multivariate and vector calculus
what prior knowledge in maths is good to go over to help me along the way in this course?
 
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Single Variable Calculus and Vectors >.<"
 
I am, by the way, a strong proponent of taking "multivariate and vector calculus" simultaneously with linear algebra.
 
I know multivariable and vector calculus, but knowing of linear algebra >.<"
 
Yep I'm also taking linear algebra
 
i'm about halfway through a multivariable and vectors course. we're about to start vectors, but for the multivariable part... know your integration. we've spent half a course so far in it.
 
dynamics said:
Hi everyone I'm just about to begin a course in multivariate and vector calculus
what prior knowledge in maths is good to go over to help me along the way in this course?

This is good to hear. I'd say that multivariable calculus was one of the most fun courses I took in college. Anyway, to answer your question, obviously all the calculus you've learned thus far is useful. But if you want specifics, I'd pay careful attention to parametric equations, arc length, coordinate systems/transformations, and the basic techniques of integration. The advanced techniques of integration that you learned back in calculus 2 will be somewhat useful, but professors don't stress this very much in multivariable calculus (they figure that if you're in this class, then you've already had enough experience with the technique of integration). If you learned the basics of vectors in either algebra or calculus 2, then review these as well. Dot products, cross products, and vector addition are important in multivariable calculus. Also brush up on determinants, since this will be very useful in finding cross products, as well as the curl of a vector.

Well, that's all I can think of right now. Good luck!
 
Sir said:
i'm about halfway through a multivariable and vectors course. we're about to start vectors, but for the multivariable part... know your integration. we've spent half a course so far in it.
Interesting! Every textbook I've seen does it the other way around: first "vectors" (f:R-> Rn) and then, later, "multivariables" (f:Rn->R).

Of course, the really fun part would be f:Rm->Rn but that requires so much linear algebra that calculus courses don't normally touch it.
 

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