Vector Calculus & Diff Equations book?

[Hobold]

Ok, the professor I got who is supposed to teach Vector Calculus and Differential Equations sucks and also does the book he uses. I am a Mechanical Engineering student and I will begin self teaching those subjects. For that matter, I would like good books, if possible. I sense those subjects are really important in engineering and I don't want to miss.

I am looking for books that are not entirely pure mathematics but also aren't totally mechanical na labour work (such as "solve this equation, now do this and you get the answer yay"). I would like to actually understand the theory behind Vector Calculus and Diff Equations but also get some applications.

Thanks in advance.

 

[Hioj]

Supposedly, https://www.amazon.com/dp/0393925161/?tag=pfamazon01-20 should be pretty good. I'm starting it soon.

For differential equations, https://www.amazon.com/dp/0486649407/?tag=pfamazon01-20 should be one of the best. It's all math, though, but seems to include lots of examples from physics. I'll start on this one soon.

 

[Hobold]

Thanks for your suggestion. That's exactly what I would like to see, physical examples with solid mathematics background.

I studied most of single variable calculus on Spivak's so I wanted something solid as well as practical.

 

[jasonRF]

Ok, the professor I got who is supposed to teach Vector Calculus and Differential Equations sucks and also does the book he uses. I am a Mechanical Engineering student and I will begin self teaching those subjects. For that matter, I would like good books, if possible. I sense those subjects are really important in engineering and I don't want to miss.

I am looking for books that are not entirely pure mathematics but also aren't totally mechanical na labour work (such as "solve this equation, now do this and you get the answer yay"). I would like to actually understand the theory behind Vector Calculus and Diff Equations but also get some applications.

Thanks in advance.

not so strong on theory, but very strong on applications (and pointing out what is important) and strong on providing you with intuition, is the free online book by Prof. Nearing:

http://www.physics.miami.edu/~nearing/mathmethods/

you can also pick up a cheap Dover edition if you like it.

 

[fourier jr]

here's what crowe wrote in his history of vector calculus:

...it may be noted that the vast majority of the authors of the books presenting the modern form of vector analysis were physicists. This is appropriate in that the great future for vector analysis lay in physical science; at present nearly all books on electricity and mechanics use vector analysis, and it appears not infrequently in books on optics and heat conduction. It is also used in many parts of modern physics, and its applications for the engineer are legion. Vector analysis has been of great value to the geometer, but geometers are few in number among modern mathematicians. Such mathematical creations as matrices, vector spaces, groups, and fields are associated only indirectly with vector analysis in the traditional sense. In many cases however their roots extend back historically to the broad system of development that culminated in the first decade of this century.

... so today I think Griffith's E&M book (or one of its equivalents) might actually be a good place to start, since it's sort of in the wilson-gibbs-coffin-maxwell-heaviside tradition. So far I've only seen good reviews & sample pages online but it looks pretty good. One day I'll get to it. Schey's is good too, and also written by a physicist even though I think it's intended to be more of a math text.

 

[Rasalhague]

I like Davis & Snider's Introduction to Vector Analysis. It has appendices on "The Vector Equations of Classical Mechanics" and "The Vector Equations of Electromagnetism" (at least the 6th edition does).

Tenenbaum and Pollard is often recommended. It has lots of examples which I imagine would make it good for practice and learning specific techiniques, but I've found it hard make progress with understanding the basic concepts. I can never tell when their x's and y's mean functions and when they mean numbers - but that might just be a personal thing...

 

[Gingia]

For vector calculus, you may want to look into Marsden & Tromba's book. It's in-between the more computationally oriented books and the more rigorous books. Also look at Hubbard & Hubbard on the topic, although their book is more for mathematics students.