Multivariable Advanced Calculus
by Kenneth Kuttler
Number of pages: 450
This book is directed to people who have a good understanding of the concepts of one variable calculus including the notions of limit of a sequence and completeness of R. It develops multivariable advanced calculus. In order to do multivariable calculus correctly, you must first understand some linear algebra. Therefore, a condensed course in linear algebra is presented first, emphasizing those topics in linear algebra which are useful in analysis, not those topics which are primarily dependent on row operations. Many topics could be presented in greater generality than I have chosen to do. I have also attempted to feature calculus, not topology. This means I introduce the topology as it is needed rather than using the possibly more efficient practice of placing it right at the beginning in more generality than will be needed. I think it might make the topological concepts more memorable by linking them in this way to other concepts.
Download or read it online for free here:
by Jerry Shurman - Reed College
A text for a two-semester multivariable calculus course. The setting is n-dimensional Euclidean space, with the material on differentiation culminating in the Inverse Function Theorem, and the material on integration culminating in Stokes's Theorem.
by Lynn H. Loomis, Shlomo Sternberg - Jones and Bartlett Publishers
Starts with linear algebra, then proceeds to introductory multivariate calculus, including existence theorems connected to completeness, integration, the Stokes theorem, a chapter on differential manifolds, exterior differential forms, etc.
by W W L Chen - Macquarie University
Introduction to multivariable and vector analysis: functions of several variables, differentiation, implicit and inverse function theorems, higher order derivatives, double and triple integrals, vector fields, integrals over paths, etc.
by Wong Yan Loi - National University of Singapore
Contents: Vector Functions; Functions of several variables; Limits and Continuity; Partial Derivatives; Maximum and Minimum Values; Lagrange Multipliers; Multiple Integrals; Surface Area; Triple Integrals; Vector Fields; Line Integrals; etc.