Multivariate and vector calculus

In summary, prior knowledge in calculus, specifically parametric equations, arc length, coordinate systems/transformations, and basic techniques of integration, as well as a basic understanding of vectors, dot products, cross products, and determinants, will be helpful in a course on multivariate and vector calculus. It is also recommended to brush up on linear algebra, as it is often taught alongside this course.
  • #1
dynamics
8
0
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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  • #2
Single Variable Calculus and Vectors >.<"
 
  • #3
I am, by the way, a strong proponent of taking "multivariate and vector calculus" simultaneously with linear algebra.
 
  • #4
I know multivariable and vector calculus, but knowing of linear algebra >.<"
 
  • #5
Yep I'm also taking linear algebra
 
  • #6
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.
 
  • #7
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!
 
  • #8
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.
 

FAQ: Multivariate and vector calculus

What is multivariate calculus?

Multivariate calculus is a branch of mathematics that deals with functions of more than one variable. It involves the study of derivatives, integrals, and differential equations in multiple dimensions.

What is the difference between multivariate calculus and vector calculus?

Multivariate calculus focuses on functions of multiple variables, while vector calculus focuses on vector fields and their derivatives. Vector calculus is a subfield of multivariate calculus that deals specifically with vector-valued functions.

Why is multivariate calculus important?

Multivariate calculus has many practical applications in fields such as physics, engineering, economics, and statistics. It allows us to understand and analyze complex systems with multiple variables and make predictions based on mathematical models.

What are some key concepts in multivariate calculus?

Some key concepts in multivariate calculus include partial derivatives, multiple integrals, gradient, divergence, and curl. These concepts are used to analyze the behavior of multivariable functions and vector fields.

How can I improve my understanding of multivariate and vector calculus?

To improve your understanding of multivariate and vector calculus, it is important to practice solving problems and working through different types of exercises. It can also be helpful to study real-world applications and examples of these concepts to see how they are used in different fields.

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