Calculus. Theory and applications. Vol. 2. (English)

Hackensack, NJ: World Scientific (ISBN 978-981-4324-27-4/hbk; 978-981-4329-70-5/pbk; 978-981-4335-71-3/hbk-set; 978-981-4335-72-0/pbk-set). xii, 410~p. (2011).

Publisher’s description: This is a book on many-variable calculus. It is the second volume of a set of two (for Vol. 1 see [Zbl 1213.26001]). It includes proofs of all theorems presented, either in the text itself, or in an appendix. It also includes a sufficient introduction to linear algebra to allow the accurate presentation of many-variable calculus. The use of elementary linear algebra in this book in presenting the topics of multi-variable calculus is more extensive than usual. It makes many of these topics easier to understand and remember. The book will prepare readers for more advanced math courses and also for courses in physical science. Supplementary materials are available upon request for all instructors who adopt this book as a course text. Contents: ‒ Matrices and linear transformations ‒ Determinants ‒ Spectral theory ‒ Vector valued functions ‒ Vector valued functions of one variable ‒ Motion on a space curve ‒ Functions of many variables ‒ The derivative of a function of many variables ‒ Optimization ‒ The Riemann integral on $\Bbb R^n$ ‒ The integral in other coordinates ‒ The integral on two dimensional surfaces in $\Bbb R^3$ ‒ Calculus of vector fields ‒ Stokes and Green’s theorems.