解析基礎２：多変数微積分（テキスト） Basic Analysis II : A Modern Calculus in Many Variables

Peterson, James K.

CRC Press（2020/07発売）

• 製本 Hardcover:ハードカバー版／ページ数 530 p.
• 言語 ENG
• 商品コード 9781138055056
• DDC分類 515.84

Full 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

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