Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach
John H. Hubbard and Barbara Burke Hubbard
A pdf version is available. Please read this before ordering.
Please consider recommending that your university or department librarian order this book. Thank you!
Why a 5th edition?
Superb on all counts — review in CHOICE (review of 1st edition)
A real gem — review of 2nd edition, MAA Monthly
Praise from readers
Review of 3rd edition, MAA Reviews
This 5th edition contains all the things that made the earlier editions different from other textbooks. Among others:
- Integrating linear algebra and multivariable calculus
- Using effective algorithms to prove the main theorems (Newton's method and the implicit function theorem, for instance)
- A new approach to both Riemann integration and Lebesgue integration
- Manifolds and a serious introduction to differential geometry
- A new way of introducing differential forms and the exterior derivative.
There is also new material, in response to requests from computer science colleagues:
- More big matrices! We included the Perron-Frobenius theorem, and its application to Google's PageRank algorithm
- More singular values! We included a detailed proof of the singular value decomposition, and show how it applies to facial recognition: "how does Facebook apply names to pictures?"