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.
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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 George Cain, James Herod
The text covers Euclidean three space, vectors, vector functions, derivatives, more dimensions, linear functions and matrices, continuity, the Taylor polynomial, sequences and series, Taylor series, integration, Gauss and Green, Stokes.
by Paul Dawkins - Lamar University
These lecture notes should be accessible to anyone wanting to learn Calculus III or needing a refresher in some of the topics from the class. The notes assume a working knowledge of limits, derivatives, integration, parametric equations, vectors.
The textbook guides students through the core concepts of calculus. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.