MATH INTRO GEN RELATIV (2ND ED) (2版)
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The book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometry-based gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences.
In the first part, the differential geometry of smooth manifolds, which is needed to present the spacetime-based gravitation theory, is developed from scratch. Here, many of the illustrating examples are the Lorentzian manifolds which later serve as spacetime models. This has the twofold purpose of making the physics forthcoming in the second part relatable, and the mathematics learnt in the first part less dry. The book uses the modern coordinate-free language of semi-Riemannian geometry. Nevertheless, to familiarise the reader with the useful tool of coordinates for computations, and to bridge the gap with the physics literature, the link to coordinates is made through exercises, and via frequent remarks on how the two languages are related.
In the second part, the focus is on physics, covering essential material of the 20th century spacetime-based view of gravity: energy-momentum tensor field of matter, field equation, spacetime examples, Newtonian approximation, geodesics, tests of the theory, black holes, and cosmological models of the universe.
Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to all the 283 exercises are included.
The second edition corrects errors from the first edition, and includes 60 new exercises, 10 new remarks, 29 new figures, some of which cover auxiliary topics that were omitted in the first edition.
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Sample Chapter(s)
Preface
Chapter 1: Smooth manifolds
Contents:
Smooth Manifolds
Tangent and Cotangent Spaces
Vector Fields and 1-Form Fields
Tensor Fields
Lorentzian Manifolds
Levi-Civita Connection
Parallel Transport
Geodesics
Curvature
Form Fields
Integration
Minkowski Spacetime Physics
Matter
Field Equation
Black Holes
Cosmology
Readership: Advanced undergraduate and beginning graduate students in Mathematics and Physics.
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Prism Reading Intro Student's Book with Digital Pack (1版)
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■ 學生課本附線上帳號 (拆封不退)
■CEFR Level: A1
■適用程度: Beginner
■隨書附線上練習,包含一篇額外閱讀文章及單字文法練習。
■線上練習平台網址:cambridgeone.org
Prism Reading Level Intro has 8 units to develop vocabulary, academic, and critical thinking skills. Students experience topics through fascinating readings in a wide variety of genres and formats to become familiar with material they might face in or outside the classroom. Each book includes a single-use code to access the Digital Pack that includes an eBook with video, Digital Workbook with extra practice to further improve reading, vocabulary, and language development, and one new reading per unit. Self-grading activities in the Digital Workbook help with learner autonomy and allow teachers to spend less time grading and more time teaching.
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