# Good books on Vectors for Newtonian mechanics?

• Classical
• christian0710
In summary, the conversation is about a person looking for a good book to learn about vectors and tensors in order to better understand classical/Newtonian mechanics. They mention being confused when physics books skip steps in vector calculations and express interest in books that provide worked examples and solutions. One book is recommended and it is mentioned that vector calculus can provide insights for certain physics problems, but it may not be necessary to fully understand it for a first mechanics course. Other books on vector calculus are also recommended for further understanding.
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.

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)?

christian0710
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.

Last edited by a moderator:
christian0710
jtbell said:
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 :)

christian0710 said:
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.

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

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.

verty said:
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?

christian0710 said:
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.)

christian0710
SredniVashtar said:
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.

## 1. What are vectors and how are they used in Newtonian mechanics?

Vectors are mathematical quantities that have both magnitude and direction. In Newtonian mechanics, vectors are used to represent physical quantities such as displacement, velocity, and force. They are essential for understanding and solving problems in classical mechanics.

## 2. What are some good books for learning about vectors in Newtonian mechanics?

Some recommended books include "Introduction to Classical Mechanics" by David Morin, "Classical Mechanics" by John R. Taylor, and "An Introduction to Mechanics" by Daniel Kleppner and Robert J. Kolenkow. These books cover the fundamentals of vectors and their applications in Newtonian mechanics.

## 3. Do I need a strong background in mathematics to understand vectors in Newtonian mechanics?

Having a basic understanding of algebra and trigonometry is helpful, but a strong background in mathematics is not necessary. Most introductory textbooks on classical mechanics assume minimal mathematical knowledge and provide explanations and examples to help readers grasp the concepts.

## 4. Are there any online resources or tutorials for learning about vectors in Newtonian mechanics?

Yes, there are many online resources and tutorials available for learning about vectors in Newtonian mechanics. Some popular options include Khan Academy, MIT OpenCourseWare, and YouTube channels such as The Organic Chemistry Tutor and Michel van Biezen.

## 5. How can I apply my knowledge of vectors in Newtonian mechanics to real-world problems?

Vectors are used extensively in various fields of science and engineering, such as physics, mechanics, and aerospace. By understanding how to use vectors in Newtonian mechanics, you can apply your knowledge to analyze and solve real-world problems related to motion, forces, and energy.

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