A friend of me who is not studying mathematics now needs to deal with integrals, double integrals and triple integrals within his study of chemistry. He asked me to give him a suggestion for a basic book that explains basic facts, rules etc., about integrals. I think this means Riemann integral and that it should not be too complicated.
I do not know such a book, do you know a book that deal with basic things concerning integrals for a non-mathematician?
Thanks for your tips!
On
Surprised to see many people endorsing Stewart. Usually it is considered incomparable with the likes of Spivak but given the context of a non-mathematical student I see the point. But I still don't think it is the best suggestion.
I think the best book to learn multi-dimensional integration from is Div, Grad, Curl, and All That - An Informal Text on Vector Calculus by H.M.Schey. It is not a chemical approach. But an electro-magnetic approach which I think the Chemistry student can relate to quite easily. It is a story-like exposition done in a beautiful sequence. It provides incentive or motivation for the Gauss and Stokes Theorems and hence makes the results easier to remember. Really is an exception to those who think these subjects cannot be understood but only memorised unless done rigorously.
But you might want to accompany it with a standard Calculus textbook too. But if you are reading Schey then you could go with something like the third volume of Marsden, Weinstein. Or even the one by Gilbert Strang which is free I think. Note these two books aren't considered friendly to non-mathematical students. But the one by Schey surely is and use these two to look up some stuff you would want to see a rigorous exposition of.
Finally there is another free MIT book called Street Fighting Mathematics which has a couple of chapters on quick integration methods. I haven't read it properly but judging by the preface I think it is made for students who want to bypass rigour.
Hope I helped.
I am one to vouch for the calculus books by James Stewart that are alluded to above by cjferes. I teach my calc courses out of these books (7E). The books are easy to understand and have quality examples. They are in color and really explain how to do the integration methods. The book has proofs, but is light on proofs. This is most likely the preferred method for a student who is not math heavy.
Another thing that is great about Stewart is that it has a large volume of diverse problems for each topic. I think this is great for self study. The odd answers are in the back of the book.
Also, there is a way to get two volumes of the single variable calc book for Stewart. The first volume is more focused on derivatives and fundamental integrals (polynomials, basic $\cos, \sin$ integrals). The second volume has a lot more about integration (by parts, trig sub, partial fractions) and engineering applications. Thus if your friend only needs some basics, volume 1 might be good. If he needs more, volume 2 can be of great use.
The multivariable book is only a single volume.