A Geometric Approach to Differential Forms 2nd ed. 2012 Edition

I used it to hold papers on my desk from blowing away until my son's birthday. I got it for him since he had it on his book list. He has a PhD in high energy physics and says it is very good. I tried reading it once but it pretty much lost me by chapter two.

I highly recommend this text for anyone looking for a "gentle" introduction to forms and manifolds.When learning a topic, I believe that it is important to develop both computational proficiency and a deep conceptual understanding. I have come to understand that manipulating symbols is not sufficient and that whenever possible, understanding the underlying geometry is critical.For whatever reason, I struggled to understand forms from other sources. (Maybe I was too focused on the algebra of the wedge product.) However, Bachmann's exposition was easy to follow and very insightful. It was a revelation that all integrands are not differential forms. Also, I had read elsewhere that forms are a basis for the tangent space of a manifold. I could say the words but they contained little meaning for me. Within the first couple of days with Bachmannn's book, this as well as some other basic ideas became crystal clear. I particularly liked that he at times presents more than one geometric interpretation of an concept.Anyone who has already seen some vector calculus and now wants a very quick introduction to forms with a minimum time investment can benefit greatly from this text. In total, I spent about a month reading, A Geometric Approach to Differential Forms and I am now confident that I am ready to tackle more advanced texts on the topic.A word of caution, in the book's Preface, it is suggested that there are three possible tracks one can take with this text. In addition to an upper division track that focuses on forms and manifolds, one is a vector calculus track and another is a multi-variable calculus track. In either of the latter two cases, if that is your main interest, I would recommend a text like Marsden's Vector Calculus. It encompasses a broader base of material and it is also very well written.

Brief yet suprisingly dense. It took the time in a few places to correct for sloppy usage of differential forms in M.T.W.'s Gravitation.

I am a graduate physics student who as such, has got a prior and long exposure to vector calculus and I was searching for a good intuitive exposition to the subject of differential forms. I also had this objective: To finally understand how the fundamental theorem of calculus, Green's theorem on the plane, Gauss Theorem of the divergence and the stoke theorem of the curl in vector calculus all arise and were diferent faces of ONE SINGLE FORMULA, namely: The "generalized" Stoke's Theorem of differential forms. I must say before anything else that after reading this book the objective was accomplished.I have found this text to be a very nice introduction to differential forms. I read it in just two weeks starting from chapter 3 to 9 (The book has 9 chapters and an Appendix), I didn't bother with the first two chapters which are a review of multivariable calculus (Calculus III).The chapters are as follow:1-Multivariable calculus, 2-Parameterizations, 3-Introduction to forms, 4-Forms, 5-Differential forms, 6-Differentiation of forms, 7-Stokes' Theorem, 8-Applications, 9-Manifolds, A-Non-linear formsI list now some of the good features that I have found about this book:i)-The author does a very clear presentation of each topic and gives plenty of intuitive explanations.ii)-It is suited for undergraduates.iii)-The book and therefore, the chapters are short making it an even easier reading.The bad features (reasons for why I gave it only four stars):iv)-Chapter 9 is different from all previous chapters, is harder and explanations aren't clear, the only drawback of the book (or perhaps is just me). To cite an example of this: The definition of a pull-back of a differential form or the section on quotient spaces.But nevermind all in all, a great place to start.

Professor Dr. Bachman is a wonderful writer. He bothers to fill in the details missing from other texts.I wish he would write a major textbook about Algebraic Topology and / or Algebraic Geometry with solutions. I would buy them.

Written to allow one to gain an intuitive understanding of form - very good for beginners such as me.

DO NOT buy the Kindle edition of this book. You will be wasting your money. The mathematical fonts are bitmapped and almost unreadable. Amazon needs to fix this problem. Buy the print edition.

I think the usefulness of this book will depend a lot on the reader's background and goals.The subject of differential forms was one of the gaps in my otherwise strong math background. More than once I started reading a differential geometry text and found myself bogged down in definitions. I chose this book in the hope of being quickly "brought on board". I was not disappointed -- in a few weeks, I finally understood what the generalized Stokes Theorem was.In my case I had a background in multivariate calculus, so skipped the initial chapters. It is not clear to me how useful this book would be to someone without that background.I feel there is one big point that the author does not adequately emphasize: a large part of the motivation for differential forms is their independence of coordinate system. The large number of numerical examples, while quite helpful, tend to obscure this point. On the other hand, to elaborate this point might have involved so much formalism as to lose me like the other books did.