Vector Calculus, Multivariable Calculus, Linear Algebra

In summary, the conversation discussed the confusion surrounding the next class after completing Calculus BC in high school. The different names for the class, vector calc and multivariable, were mentioned, with the clarification that they are essentially the same subject. There was also discussion about whether linear algebra is necessary for this class, with varying opinions on its importance. Ultimately, it was suggested to take whichever class seems more interesting and to consider taking honors math courses in college for those interested in theoretical physics.
  • #1
member 508213
I am in Calculus BC in high school right now and I am really enjoying it and have finished all of the material for the year and I have heard different things about what class comes after Calculus BC (I believe BC is equivalent to Calc 1 & 2 in college). I have heard the next class, aka Calc 3, is vector calc from some sources and multivariable from others and I am wondering if these subjects are similar? and what differences? and what comes first typically?

Additionally, I have heard that you need linear algebra for vector and multivariable so I am wondering if THAT comes first?? Basically I am confused on what I should focus on now that I have finished Calc 2.

I have tried to look up what comes next, but again I am getting mixed answers. Any help telling me the similarities and differences and what I should study first would be of great help!

Thanks!
 
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  • #2
Austin said:
is vector calc from some sources and multivariable from others and I am wondering if these subjects are similar?

They're two names for the same thing.

Austin said:
I have heard that you need linear algebra for vector and multivariable

I think at some schools you do, at others you don't. At the college where I work, linear algebra is not a prerequisite for vector calc. I would say go ahead and do whichever one looks more interesting to you. Vector calc is of course more directly related to the other calculus you've studied.
 
  • #3
I suggest you take honors math courses once in college if you really want to work on theoretical physics. Just a thought.
 
  • #4
TimeInquirer said:
I suggest you take honors math courses once in college if you really want to work on theoretical physics. Just a thought.
? I don't want theoretical physics what does that have to do with this thread?
 
  • #5
This is "Physics Forums", after all. :oldwink: People tend to assume you're going to be a physics major unless you say otherwise.
 
  • #6
jtbell said:
This is "Physics Forums", after all. :oldwink: People tend to assume you're going to be a physics major unless you say otherwise.
Nah I'm just here to ask a math question :)
 
  • #7
I suppose you are right. Still, take the honors classes lol
 

What is Vector Calculus?

Vector calculus is a branch of mathematics that deals with the study of vector fields and their derivatives, such as gradient, divergence, and curl. It is used to describe and analyze physical phenomena in three-dimensional space.

What is Multivariable Calculus?

Multivariable calculus is a branch of mathematics that extends the principles of calculus to functions of multiple variables. It involves the study of partial derivatives, multiple integrals, and vector-valued functions.

What is Linear Algebra?

Linear algebra is a branch of mathematics that deals with the study of vector spaces and linear transformations between them. It involves the analysis of systems of linear equations, matrices, determinants, and eigenvalues and eigenvectors.

How are these topics related?

Vector calculus, multivariable calculus, and linear algebra are all closely related and often used together in mathematics and science. Linear algebra provides the foundation for understanding vector calculus, which in turn is used in multivariable calculus to solve problems involving multiple variables.

What are the practical applications of these topics?

These topics have a wide range of practical applications in various fields such as physics, engineering, computer graphics, economics, and statistics. They are used to model and analyze physical systems, optimize functions, and solve real-world problems involving multiple variables and equations.

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