Best Multivariable Calculus Textbooks: Pros, Cons, and Recommendations

In summary, the conversation revolves around finding a good vector/multivariable calculus textbook. Greetz is looking for recommendations and personal experiences with different textbooks, mentioning Marsden & Tromba and Stewart's "Calculus: Early Vectors." Perion suggests Stewart's 5th edition and also mentions Kaplan's "Advanced Calculus." They also discuss the book "Div, Grad, Curl, and All That" and its usefulness. Perion ends up choosing "Multivariable Calculus: Concepts and Contexts" and mentions using Mathematica for lab work.
  • #1
Perion
Greetz,

I'm trying to find a vector/multivarible calculus textbook that impressed folks that used it. I'd appreciate any pros or cons of any that you've personnaly used. I can get Marsden & Tromba at abebooks.com used & VERY cheap but too many people think that text sux (at amazon.com reviews). Most of them seem to prefer one by Stewart but if they're referring to "Calculus : Early Vectors" by James Stewart, then I can't find it for under $100 - much more than I'd like to spend. Besides, half that book just seems like Calc I stuff (though the presentation of the material does seem to be of extraordinary quality).

[Also, I'll probably buy the textbook with "Div, Grad, Curl, and All That" - any comments on that book?]


Thanks,
Perion
 
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  • #2
I've got Stewarts 5th edition "multivariable calculus". You can buy just the latter half (calc 3 and 4) of the stewart's books alone, the expensive ones are calc 1 -4. My book was 70$, not too bad in hawaii.

It's not impressive (what calculus text is? What one fool can do can another can do, right?) , but it is exceptionally readable.

Also, if you are just trying to learn the stuff, there are no secrets unlocked in Div, Grad, curl... that won't be repeats of what is in a full multivariable textbook.
 
  • #3
As someone whose required textbook was Marsden and Tromba, I'll stand by what the people at Amazon told you. It was not that great a book, IMO.
 
  • #4
Wilfred Kaplan, "Advanced Calculus"

I have an extra copy if you are interested, its in almost-perfect condition though, so it might be too pricey.
 
  • #5
Thanks for the input.

I ended up going with "Multivariable Calculus : Concepts and Contexts" - 2nd Edition. It had excellent reviews and found it (new) for $45. It's always a gamble...

Also downloaded some good Mathematica lab courses for multivariable calc; hoping to be able to combine the lab stuff with textbook study and someday get a handle on vector fields.

Happy Friday!
Perion
 

1. What is vector calculus?

Vector calculus is a branch of mathematics that deals with the differentiation and integration of vector fields, which are mathematical functions that assign a vector to every point in space.

2. What topics are typically covered in a vector calculus textbook?

A vector calculus textbook typically covers topics such as vector algebra, vector functions, gradients, divergence, curl, line integrals, surface integrals, and the theorems of Green, Stokes, and Gauss.

3. What are some real-life applications of vector calculus?

Vector calculus has many applications in science and engineering fields, such as fluid mechanics, electromagnetism, computer graphics, and economics. It is used to model and analyze physical phenomena, such as fluid flow, electric fields, and economic markets.

4. Is vector calculus difficult to learn?

This may vary for each individual, but vector calculus can be challenging because it involves both vector and scalar quantities, as well as different types of integrals and theorems. However, with practice and a solid understanding of basic calculus, it can be learned effectively.

5. Are there any resources or supplemental materials available to help with learning vector calculus?

Yes, there are many resources available such as online tutorials, practice problems, and video lectures. Many textbooks also come with solution manuals and online resources for additional practice and support. It may also be helpful to seek out a tutor or attend study groups for extra help and clarification.

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