A modern calculus in many variables
Author(s)
Bibliographic Information
A modern calculus in many variables
（Basic analysis / James K. Peterson, 2）
CRC Press, 2020
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Note
Includes bibliographical references (p. 505-506) and index
Description and Table of Contents
Description
Basic Analysis II: A Modern Calculus in Many Variables focuses on differentiation in Rn and important concepts about mappings from Rn to Rm, such as the inverse and implicit function theorem and change of variable formulae for multidimensional integration. These topics converge nicely with many other important applied and theoretical areas which are no longer covered in mathematical science curricula. Although it follows on from the preceding volume, this is a self-contained book, accessible to undergraduates with a minimal grounding in analysis.
Features
Can be used as a traditional textbook as well as for self-study
Suitable for undergraduates in mathematics and associated disciplines
Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
Table of Contents
1. Beginning Remarks 2.Preliminaries 3.Vector Spaces 4.Linear Transformations 5.Symmetric Matrices 6.Continuity and Topology 7.Abstract Symmetric Matrices 8.Rotations and Orbital Mechanics 9.Determinants and Matrix Manipulations 10.Differentiability 11.Multivariable Extremal Theory 12.The Inverse and Implicit Function Theorems 13.Linear Approximation Applications 14.Integration in Multiple Dimensions 15.Change of Variables and Fubini's Theorem 16.Line Integrals 17.Differential Forms 18.The Exponential Matrix 19.Nonlinear Parametric Optimization Theory 20.Summing It All Up. References. Index
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