Where Can I Find Useful Resources for Vector Calculus?

[Macgyver]

I am in a vector calculus class with a teacher that lectures from the book (and gives very few examples) and a book that is of little help.

Do any of you know some helpful online resources (or inexpensive books) for higher level calculus?

 

[Dr Transport]

There is a Schaum's Outline in Vector Analysis which covers a majority of what you will ever need. Do a Google search on vectors and you find a bunch of material out there. Almost every course in physics starts with some type of refresher in vectors, just look online for notes.

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[vadik]

I learned a lot of vectors in Stanley I. Grossman's book "Multivariable calculus, Linear algebra and Differential equations" Though the book might be expensive.

 

[matt grime]

As someone who's had to teach from these god awful books and encountered attitudes such as this, do you , Macguyver (Patty and Selma would approve), realize that these ideas and examples are trivially dull and easy? How many of the worked examples have you started and gone through, looking back at the method when you get stuck? All the things you are looking at are simple formulae that require no understanding of what's going on, and if you think you need to understand in some higher meta-sense then it is because you aren't understanding that you do not need to understand what, say, grad(f) is to calculate grad(f), it's just a bloody formula, and that through working it out a few times, only then will you understand what the formula means.

 

[Macgyver]

Matt, I'm not in need of the examples as much as I am the explanation of the definitions and th methods. I have trouble remembering how to do something if I don't understand what I am doing and why. To me a definition without the reasoning behind it is usless since i can't adapt it to a specific problem. I didn't mean for it to sound like i was blaming my professor for my confusion.

 

[matt grime]

Once you know the method it works for all cases, that is one of the nice things about calc. IT just takes practise and memeory.

 

[vadik]

It is up to yourself will you understand things deeper or not. When there's a definition or a theorem in a book you might just agree with it or think for a while to understand what does it really mean.

 

[matt grime]

If I may interject with a slightly dubious analysis, did you ever learn a foreign language? Did you ask why? When you were told the word for breakfast did you quesytion why, what does it mean that petit dejeuner (or whatever) is breakfast in French? No, you didn't, you learned the words, and the rules and mathematics is no different, you're just learning a language and its use.There are no big metaphysical things going on, no ontological debates about why this is what it is, they're just definitions that you need to apply. Later you might learn how to apply it from people who have specific uses in mind, but it is not relevant to the learning of how to do things. One general formula is worth a thousand worked examples.

 

[vadik]

What I meant is like, when you see a definition of a derivative [f(x+h)-f(x)]/h, you don't just remember by heart "ef ex plus eich minus ef ex divided by h" and say "I know what derivative is", but you try to understand what the equation contains and finally understand that it means the velocity of function's changing or however to interpret. Even if it's not told in the book that it is shows the velocity, you can figure it out with a little thinking.

 

[Ebolamonk3y]

which also ties into the Fundamental theorem of Calculus... Where you state that d/dx of antiderivative of f(x) is f(x)...

 

[Ebolamonk3y]

If there is not a deep feeling for the workings of the equations... then how did Srinivasa Ramanujan "see" these wonderful series and stuff in his head? Its a deep understanding alright...