Calculus and Analysis in Euclidean Space

• Main Author: Shurman, Jerry (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Analysis.

The graceful role of analysis in underpinning calculus is often lost to their separation in the curriculum. This book entwines the two subjects, providing a conceptual approach to multivariable calculus closely supported by the structure and reasoning of analysis. The setting is Euclidean space, wit...

Table of Contents:

• Preface
• 1 Results from One-Variable Calculus
• Part I Multivariable Differential Calculus
• 2 Euclidean Space
• 3 Linear Mappings and Their Matrices
• 4 The Derivative
• 5 Inverse and Implicit Functions
• Part II Multivariable Integral Calculus
• 6 Integration
• 7 Approximation by Smooth Functions
• 8 Parameterized Curves
• 9 Integration of Differential Forms
• Index.