**Vector Calculus, Linear Algebra, and Differential Forms 5th Edition, ISBN-13: 978-0971576681**

[PDF eBook eTextbook]

- Publisher: Matrix Editions; 5th edition (January 1, 2015)
- Language: English
- 818 pages
- ISBN-10: 0971576688
- ISBN-13: 978-0971576681

This text covers most of the standard topics in **multivariate calculus** and part of a **standard first course in linear algebra**. It focuses on underlying ideas, integrates theory and applications, offers a host of pedagogical aids, and features coverage of differential forms and an emphasis on numerical methods to prepare students for modern applications of mathematics. * Covers important material that is usually omitted. * Presents more difficult and longer proofs (e.g. Proofs of the **Kantorovitch theorem**, the implicit function theorem) in an appendix. * Makes a careful distinction between vectors and points. * Features an innovative approach to the implicit function theorem and inverse function theorem using Newton’s method. * Always emphasizes the underlying meaning – what is really going on (generally, with a geometric interpretation). The chain rule is a composition of linear transformations; the point of the implicit function theorem is to guarantee that under certain circumstances, non-linear equations have solutions. * Integrates theory and applications. * Begins most chapters with a treatment of a linear problem and then shows how the 7 methods apply to corresponding non-linear problems.

**John H. Hubbard** (BA Harvard University, PhD University of Paris) is professor of mathematics at Cornell University and at the University of Provence in Marseilles he is the author of several books on differential equations. His research mainly concerns complex analysis, differential equations, and dynamical systems. He believes that mathematics research and teaching are activities that enrich each other and should not be separated.

**Barbara Burke Hubbard** (BA Harvard University) is the author of The World According to Wavelets, which was awarded the prix d’Alembert by the French Mathematical Society in 1996.

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