![]() ![]() Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach by Hubbard and Hubbard. That being said, here are a few that I like in no particular order: There are many great books that cover multivariable calculus/analysis, but I'm not sure a "standard" really exists. To my mind, the intricacies of such processes are not fully realized until one studies the integration of differential forms on differentiable manifolds. In vector calculus, one discusses line integrals and surface integrals of both functions and (co)vector fields. The theory of curves and surfaces leads naturally towards Riemannian geometry, though certainly other branches of geometry also generalize this subject. This can be generalized to multiple Lebesgue integration via consideration of product measures. One of the most widely-used is Differential Geometry of Curves and Surfaces by do Carmo, though I highly recommend Elementary Differential Geometry by Pressley.Ī few remarks as to where these topics end up going, with a slant towards differential geometry:ĭifferentiation of functions $f\colon \mathbb$. Actually, this text also discusses integration and vector calculus (Chapter 10), but I personally found Rudin's treatment of such hard to follow when I was first learning the subject.įor differentiation, integration, and vector calculus you can use Calculus on Manifolds by Spivak, or Analysis on Manifolds by Munkres.įor curves and surfaces, you can use basically any book on elementary differential geometry. Vector Calculus (Green's Theorem, Stokes' Theorem, Divergence Theorem)įor differentiation, you can use Principles of Mathematical Analysis by Rudin (Chapter 9).Psalms 83:18.I usually think of multivariable calculus as being divided into four parts: ![]() *Jehovah is the personal name of Almighty God. What really helps too, is if you have a good AP Calculus teacher. The Free Response Questions on the AP tests are much different then those at the end of chapter exercises in the textbooks so practice with the old AP tests as much as possible - this is my modest opinion anyway. There is a focus on the Integral as an Accumulation Function right now on these tests. But as soon as you can, begin working the test questions on old AP tests published on their website (College Board) so that you will have a feel for the test questions and styles. ![]() My suggestion is to use the required text for your class, but get a used supplement like Princeton’s and work problems and exercises as much as possible. But these will probably come later for you. If your planning to teach math some day, the “old school” Calculus books by Spivak, Taylor, or Apostol, and others may be of interest to you. Another book that is liked is Calculus With Analytic Geometry by George Simmons but this is a $200.00 book new. However, the AP sections and questions are somewhat weak and not up to the level of thinking and reasoning required for the AP tests. The book used at the school where I work is Larson’s and Edward’s Ninth (9th) edition, AP edition. I’ve been looking for that special math (Calculus) book for some years now and have not found it - you know - that math book that is almost like Jehovah’s* Holy Bible: that is refreshing, readable, understandable, just pure delight to read and study. Most of the Math books are pretty much the same and hard to learn from at times…but you can still learn from them if your up to the challenge. But many of the books mentioned above are well known and used in their so-called ‘AP Editions’ in AP classes. Well, I don’t think this is an answerable question - definitively anyway. ![]()
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