# Advice on studying vector calculus

#### Quasar Chunawala

Hi all,

I am currently taking a course on Vector calculus. I am using two books - Vector analysis by Louis Brand and Vector Calculus by Susane J Colley, I am solving all of the exercises.

1. When you guys studied vector/multivariable calculus, what textbooks did you like? What is your review of the above two books?
2. To build more intuition, I am also solving a few problems from the first year introductory physics book, Kleppner, Kolenkow. Does that sound like a good idea? Would you know of any other sources containing a great collection of applied problems?
3. Any other tips to be successful in this subject.

Cheers,
Quasar.

#### Daniel Duffy

##### C++ author, trainer
The Schaum Vector Analysis in 2d and 3d is good (it is also focused on maths physics applications).

It is a springboard for the n-dimensional generalizations in Opimisation and Machine Learning.

Hands-on (Schaum is best) is important for LTM learning.

#### Quasar Chunawala

The Schaum Vector Analysis in 2d and 3d is good (it is also focused on maths physics applications).

It is a springboard for the n-dimensional generalizations in Opimisation and Machine Learning.

Hands-on (Schaum is best) is important for LTM learning.

Thanks Daniel, anything I can take up as a project? Any ideas?

I am afraid I don't know what LTM stands for.

#### Daniel Duffy

##### C++ author, trainer
LTM == Long Term Memory

Why try implementing a simple version of

I am using two books - Vector analysis by Louis Brand and Vector Calculus by Susane J Colley, I am solving all of the exercises.

The Brand book belongs to the era of the Flintstones (probably the book Fred used when he attended Bedrock University). The Colley book is one of the best current treatments of vector calculus, particularly the final chapter, which deals with differential forms and Stokes theorem in the language of forms.

#### Daniel Duffy

##### C++ author, trainer
Fred's car was easy to maintain (and check out those zebra seats)

The danger of forms is loss of physical intuition. Almost Bourbaki.

I like Murray Spiegel

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#### Quasar Chunawala

The Brand book belongs to the era of the Flintstones (probably the book Fred used when he attended Bedrock University). The Colley book is one of the best current treatments of vector calculus, particularly the final chapter, which deals with differential forms and Stokes theorem in the language of forms.
Cool! Thank you so much for this assertion. I really like the text. I was reading this chapter on vector-valued functions and their derivatives. At one place, the author derives Kepler's laws of planetary motion using vector derivatives. Its well presented, except that it's not entirely intuitive to me. That threw me off.

To elaborate, its been a while, since I got back to freshman physics. I have studied high-school physics earlier. While I completely understood each step algebraically, the proof feels like a bunch of mathematical jugglery. The physical meaning of the constant vectors like $$\vec{c}$$ and $$\vec{d}$$ used in the proof aren't clear to me. Like, it isn't something I could come up on my own. At which point, I began to stray to other texts, losing energy and momentum.

I wrote in my own words, the derivation in the book here(I created a .TeX & converted to PDF), just in case you folks have any views on it.

#### Attachments

• Kepler's laws of planetary motion.pdf
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#### Quasar Chunawala

Fred's car was easy to maintain (and check out those zebra seats)

The danger of forms is loss of physical intuition. Almost Bourbaki.

I like Murray Spiegel

That picture sure is hillarious! :D

I will buy a copy of Murray Spiegel's book. It has plenty of examples I guess, and is great for brushing up later on as well.

#### Daniel Duffy

##### C++ author, trainer
That picture sure is hillarious! :D

I will buy a copy of Murray Spiegel's book. It has plenty of examples I guess, and is great for brushing up later on as well.
Lots of examples, indeed.

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