Learn Vector Calculus With This Book

There are not that many books that are completely devoted to the subject of Vector Calculus. In this video I will show you a book that is devoted to this beautiful area of mathematics which you can use for self-study or to supplement your current Calculus course. The book is titled Vector Calculus and it was written by Susan Jane Colley.

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[rithikkhanna]

I don't think you mentioned the best part of this book: She fully covers functions from m-space to n-space, leading her to define the derivative as a Jacobian Matrix, use the Hessian to classify critical points, and state the Change of Variables Theorem in full generality. This is my favorite book for multivariable differential calculus; for integral calculus, I prefer Bray's Multivariable Calculus.

[benhill]

I have this exact edition. It was 6.69 U.S.D. when I got it, but It was free for me because I applied some reward points from the website where I ordered this book. Indeed, I couldn't find other vector calculus books at the time. I'm glad to see this is a great resource for learning vector calculus when I'm ready for it. Thanks!

[jonmartin]

You have no idea how much you've made me spend on books this month. I need a new bookshelf already and this looks like another text I need to get :)

[vnever]

Hey Math Sorcerer, great review as usual. Another great book on the same topic is _Vector Analysis_ by Homer E. Newell Jr.
Great text with many physical applications and yet a thorough mathematical treatment!

[themessiahcodemovement]

Thank you sir I really appreciate you sharing your knowledge it is helping me grow in my mathematics

[arims]

tysm!! i'm a mechatronics engineering major and just now i'm (finally) in calculus 3 and i was looking for book recommendations. Truly thankful to give the spotlight to hidden treasures :D

[minimalrho]

I've always stopped at Green's theorem when teaching Calc 3, never getting into surface integrals. Maybe because I'm teaching at a community college, but the pacing is hard to get any more material in that class beyond that. The idea of going through all of vector calculus in that class boggles my mind.

[madhavpr]

This is a beautiful book. The fourth edition has an additional chapter on differential forms. Great stuff!! :D I keep going back to this book for refreshing my knowledge about anything related to multivariable calculus (especially the three big theorems of vector analysis- Green, Gauss and Stokes) and physics (mechanics or electromagnetism).

[AceOfHearts]

Love this type of layout. Considerate to the learner.

[Taylor-rxyb]

Wow differential forms! I don't think I've ever seen those discussed in a calculus text (well explicitly at least). Awesome book!

[billmorrigan]

I have the 4th edition. It's an excellent book. Standard calculus books have 1000+ pages but vector calculus and multiple variables are not as deeply and comprehensively covered as in this book. Multiple variables are of course a much more advanced part of calculus. This book nails it providing comprehensive coverage. It's just like ODE are not covered deeply either in calculus books. You need a separate book for that. Unfortunately, they are not that many good books on vector calculus. This is a must-have book for those who want to gain a superior and advanced knowledge of calculus. It blows out of the water any standard calculus book when it comes to multiple variables and vector calculus (Calc 3 and 4). This book is my top recommendation for those who want to master calculus very deeply at a serious level. However, there's no ODE in it but Boyce DiPrima's book solves that.
By the way, Colley has some good book recommendations at the end of her _Vector Calculus._ It's not just a haphazard list of books. It's a well structured recommendation of important math books.

It is worth mentioning that analytic geometry has been severely reduced. Its remnants are now part of calculus. However there's a good separate book on analytic geometry too. It's by Douglas. It's also very expensive. Analytic geometry should precede vector calculus. Luckily, there are electronic versions of books nowadays and ridiculous price tags can be avoided.

[alexgian]

Good call, this book!
As a refresher, but also as a preparation for DG I found it hit the spot. Thanks.
Thinking of doing Morgan's Riemannian Geometry after this.

[evionlast]

This book is very good for self learning you'll have a sequence of exercises that is very instructive from practical calculation to theory development, I'll say you'd want to do more after this naturally it's very introductory.

[thomasblackwell]

“Vector Calculus” by Marsden and Tromba is absolutely great!

[John_Smith__]

Teach what you can and teach well ...wise words no doubt.

[timduncankobebryant]

I teach my classes using Shifrin multivariable calculus. It's a bit more rigorous.

[guidichris]

Again, look for the 2nd or 3rd editions. 2nd edition can be had for under $35, whereas the current edition is 145 used. Nice thing about self study is you don't have to have the most current edition.

[dimitrioskalfakis]

essential math for engineers. good stuff. rough seas ;-)

[hikaryagravity]

This book cover looks like so much like an amazing science-fiction book !

[davidmata]

I recommend "Introduction to Vector Analysis" by Harry F. Davis and Arthur David Snider. It's a book designed for upper-division courses and covers topics not normally covered in Calc. 3 courses, such as tensors and orthogonal curvilinear coordinates. It's also heavy on physics applications.