Differential Calculus and Its Applications

✍ Scribed by Michael J. Field

• Publisher: Dover Publications
• Year: 2012
• Tongue: English
• Leaves: 583
• Edition: Reprint
• Category: Library

✦ Synopsis

This text offers a synthesis of theory and application related to modern techniques of differentiation. Based on undergraduate courses in advanced calculus, the treatment covers a wide range of topics, from soft functional analysis and finite-dimensional linear algebra to differential equations on submanifolds of Euclidean space. Suitable for advanced undergraduate courses in pure and applied mathematics, it forms the basis for graduate-level courses in advanced calculus and differential manifolds.
Starting with a brief resume of prerequisites, including elementary linear algebra and point set topology, the self-contained approach examines liner algebra and normed vector spaces, differentiation and calculus on vector spaces, and the inverse- and implicit-function theorems. A final chapter is dedicated to a consolidation of the theory as stated in previous chapters, in addition to an introduction to differential manifolds and differential equations.

✦ Table of Contents

PREFACE
CHAPTER 0 PRELIMINARIES
CHAPTER 1 LINEAR ALGEBRA AND NORMED VECTOR SPACES
CHAPTER 2 DIFFERENTIATION AND CALCULUS ON VECTOR SPACES
CHAPTER 3 THE INVERSE- AND IMPLICIT-FUNCTION THEOREMS
CHAPTER 4 DIFFERENTIAL MANIFOLDS
BIBLIOGRAPHY
INDEX

✦ Subjects

Calculus, Mathematics