Terrance Said:

What comes first, Multivariable Calculus or Vector Calculus?

We Answered:

These terms (multivariable and vector) are often used interchangeably to refer to the same subject. This, from Wikipedia: The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which includes vector calculus as well as partial differentiation and multiple integration.

The introductory vector calculus books that I've encountered actually include sections on partial differentiation and multiple integration. So an introductory course in either of these topics will cover essentially the same material.

Corey Said:

What is the difference bt James Stewart's "Calculus" & "Calculus: Early Transcendentals"? Which is better?

We Answered:

Typically exponential functions, being e^x and ln(x), are introduced later in the text after differentiation and integration are already exposed and discussed in detail. This is because the exponential and logarithmic functions can be more easily defined with the use of those techniques.

An "Early Transcendentals" book, covers these functions from the beginning and uses them, and assigne exercises with them from the get go, even when differentiation and integration are being taught and used for the first time. The reason for this book is if a certain curriculum is designed this may. For example, maybe engineers or physicists need to know about these functions right away, so may they should take a course that covers these as soon as possible.


It only makes a difference in the earlier, say the first seven or so chapters, in a book with likely around sixteen chapters, so it makes little different in the big scheme of things, especially once you get to multivariable calculus.

I would sugest that you make sure the book is the full version (the list price should be around $135), and not just the first volume, otherwise you won't get the multivarible stuff in the same book.

I used the normal version of Stewart and it was fine if you don't need to know much about the theoretical background (but even Stewart dips a bit into proofs and such).

I would suggest you get the normal version too (especially if you don't really understand the difference) if you're teaching yourself, as there's no reason getting the less commonly used verison, as most courses that I know of are not structured with an early transcendentals syllabus.

Megan Said:

Calculus books?

We Answered:

I like Calculus Early Transcendentals
James Stewart 6th edition
ISBN-13: 978-0-495-38343-7

There is also a complete solutions manual
ISBN-13: 978-0-495-01255-9

I got my books at half.com for $60 each
If they don't have them there you can probably find them at Amazon.com but they will cost a lot more.

I tutor Math and Chem for a living so I think I can judge a book pretty well.

Good luck to you
hope this helped!!!

Ricardo Said:

What is multivariable calculus?

We Answered:

Multivariable calculus deals with functions of more than one variable.
z = f(x,y) for instance
Where z depends on both x and y
You can also have multiple outputs of these functions
(u, v) = ( f(x ,y) , g(x,y) )
And any other number of inputs and outputs.
This can be used to describe vector fields.
You can then use MVC to prove that a field is conservative or not. For instance that the gravitational field of an object is conservative.

It's been a while since I took this class. I remember that you learn how to find flux through a surface, as in electric flux or water flow through a surface. You can use MVC to find the surface area.

That's all I remember off the top of my head.
I found the class interesting. But then again, I'm a mathematician not an engineer.

Alexander Said:

Is Multivariable calculus even useful for a career in economics, finance, or business?

We Answered:

I was a Mathematics major, but later in life went into the accounting field. In my 25+ years of doing that, I have never had the need to apply multivariable calculus. However, I think that studying math does in fact train you to think critically and precisely about problems/situations. In that sense, it is indeed a worthwhile activity.