Good books on Vectors for Newtonian mechanics?

[christian0710]

Hi, I'm internested in a good book that teaches vectors (and perhaps tensors?) so i can better understand books on classical/Newtoniam mechanics.

I know the basics of vectors, but i still get confused when i se them in physics books and don't completely understand what's going on when physics books skip steps in vector calculations.
I'd love some good books on that subject.

 

[jtbell]

Do you mean vector algebra (components, unit vectors, dot product, cross product) or vector calculus (the things that use the ∇ operator, like divergence, gradient, curl)?

 

[verty]

Books on vectors tend to be really difficult. There are at least 4 for sale on Amazon that I think are too difficult for you. I say this because I've seen about 10 of these posts of yours asking for books and in almost every one you say you like worked examples and, if possible, solutions.

Luckily, this one looks to be at the right level: https://www.amazon.com/dp/0071615458/?tag=pfamazon01-20.

PS. I assume you meant vector calculus. Perhaps I shouldn't have assumed this.

 

[christian0710]

Do you mean vector algebra (components, unit vectors, dot product, cross product) or vector calculus (the things that use the ∇ operator, like divergence, gradient, curl)?

Do you know if vector calculus is used in Classical mechanics? If it's useful to learn I'll be glad to learn about it, but I'm a beginner :)

 

[verty]

Do you know if vector calculus is used in Classical mechanics? If it's useful to learn I'll be glad to learn about it, but I'm a beginner :)

Vector calculus is basically calculus done in n dimensions. So it is quite abstract but I find that it's a nicer way to learn multivariable calculus. You have already bought calculus books so strictly speaking you would never need to learn vector calculus as such. What you would need you would learn in those other books. That said, for me personally, I prefer the abstraction of n-dimensions.

To answer your question, there are times when insight could be gained by knowing vector calculus. An example is centripetal acceleration, why does it point to the center of the circle? It's nice to represent the motion by a vector function and then differentiate the function twice to get the acceleration, and then you would see that it points toward the center.

On the integration side of things, it is less clear that there is any advantage. Probably what I would recommend is to learn the algebra and the differentiation parts only. Or you could just learn the algebra topics. That Schaum's book does include the algebra topics at the start of the book.

 

[jasonRF]

I second the recommendation of the Schaum's outline on vector analysis - I purchased an earlier edition while taking mechanics and it certainly helped. It included vector valued functions of a single variable, which is very useful in mechanics. It was useful in a number of later courses as well, especially electrodynamics. The part of the book on tensors was pretty uninspiring, though.
jason

 

[vanhees71]

For a first mechanics course (point particles) from vector calculus you just need the gradient for conservative forces. I'd leave the full machinery of vector calculus for the next semester when you start with electrodynamics.

 

[christian0710]

Vector calculus is basically calculus done in n dimensions. So it is quite abstract but I find that it's a nicer way to learn multivariable calculus. You have already bought calculus books so strictly speaking you would never need to learn vector calculus as such. What you would need you would learn in those other books. That said, for me personally, I prefer the abstraction of n-dimensions.

To answer your question, there are times when insight could be gained by knowing vector calculus. An example is centripetal acceleration, why does it point to the center of the circle? It's nice to represent the motion by a vector function and then differentiate the function twice to get the acceleration, and then you would see that it points toward the center.

On the integration side of things, it is less clear that there is any advantage. Probably what I would recommend is to learn the algebra and the differentiation parts only. Or you could just learn the algebra topics. That Schaum's book does include the algebra topics at the start of the book.

Hi Verty, Thank you very much for the recommendation and explanation! That Schaums book looks very good for problem solving which i definitely need. Does it also do a good job in giving intuition to why vector calculus and vector algebra is useful and how to interprete it, perhaps visually and in terms of physics problems? Or is there an other book for that?

 

[verty]

Hi Verty, Thank you very much for the recommendation and explanation! That Schaums book looks very good for problem solving which i definitely need. Does it also do a good job in giving intuition to why vector calculus and vector algebra is useful and how to interprete it, perhaps visually and in terms of physics problems? Or is there an other book for that?

You said you were reading physics books and the vector calculations were confusing you. This book will have probably every vector calculation you are likely to see with a worked example. So I don't see why you need this other stuff. It solves the problem you asked in the original post.

(I don't know if it gives intuition or not.)

 

[SredniVashtar]

Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (Fourth Edition)
A Student's Guide to Vectors and Tensors

I don't know why all text look so big...
The more these web platforms evolve, the less they are manageable.

EDIT: fixed, thanks to Fredrik's suggestion.

 

[Fredrik]

I don't know why all text look so big...

Your post contains BB code tags that set the size to 6. You can see them if you hit the edit button (or the reply button if the time limit for edits has passed), and then the symbol that looks like a piece of paper with writing on it, in the upper right corner.