数理物理学の構造（テキスト） The Structures of Mathematical Physics : An Introduction （2021）

Starkovich, Steven P.

Springer Nature Switzerland AG（2022/07発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 258 p.
• 言語 ENG
• 商品コード 9783030734510

Full Description

This textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups --- mathematical structures which are foundational to modern theoretical physics. It is aimed primarily at undergraduate students in physics and mathematics with no previous background in these topics. Applications to physics --- such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equations and the Generalized Stokes's Theorem --- appear at appropriate places in the text. Worked examples, end-of-chapter problems (many with hints and some with answers) and guides to further reading make this an excellent book for self-study. Upon completing this book the reader will be well prepared to delve more deeply into advanced texts and specialized monographs in theoretical physics or mathematics.

Contents

Preface and Acknowledgements.- Sets and Relations.- Mappings and Functions.- Rings and Fields.- Linear Vector Spaces.- Algebras.- Basic Topology and Topological Groups.- Topological Vector Spaces.- Measure, Integration and Hilbert Space.- Operators and Spectra.- Annotated Bibliography and a Guide to Further Reading.- Index.