Introduction to Geometry and Relativity

David C. Mello, PhD
Department of Mathematics, John Hazen White School of Arts & Sciences, Johnson & Wales University, Providence, Rhode Island, USA

Series: Mathematics Research Developments, Physics Research and Technology
BISAC: MAT027000

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Volume 10

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Special issue: Resilience in breaking the cycle of children’s environmental health disparities
Edited by I Leslie Rubin, Robert J Geller, Abby Mutic, Benjamin A Gitterman, Nathan Mutic, Wayne Garfinkel, Claire D Coles, Kurt Martinuzzi, and Joav Merrick

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This book provides a lucid introduction to both modern differential geometry and relativity for advanced undergraduates and first-year graduate students of applied mathematics and physical sciences. This book meets an overwhelming need for a book on modern differential geometry and relativity that is student-friendly, and which is also suitable for self-study. The book presumes a minimal level of mathematical maturity so that any student who has completed the standard Calculus sequence should be able to read and understand the book.

The key features of the book are:
– Detailed solutions are provided to the Exercises in each chapter.
– Many of the “missing steps” that are often omitted from standard mathematical derivations have been provided to make the book easier to read and understand.
– A detailed introduction to Electrodynamics is provided so that the book is accessible to students who have not had a formal course in this area.
– In its treatment of modern differential geometry, the book employs both a modern, coordinate-free approach and the standard coordinate-based approach. This makes the book attractive to a large audience of readers.
Also, the book is particularly attractive to professional non-specialists who would like an easy to read introduction to the subject. (Imprint: Nova)

Preface pp. i-xiii

Chapter 1. Introduction to Newtonian Spacetime pp. 1-10

Chapter 2. The Structure of Newtonian Spacetime pp. 11-28

Chapter 3. Maxwell's Equations pp. 29-76

Chapter 4. Introduction to Special Relativity pp. 77-110

Chapter 5. Introduction to Differential Geometry pp. 111-156

Chapter 6. Tensor Calculus pp. 157-226

Chapter 7. Introduction to Minkowski Space pp. 227-248

Chapter 8. Maxwell's Equations in Minkowski Space pp. 249-270

Chapter 9. Relativistic Hydrodynamics pp. 271-288

Chapter 10. Foundations of General Relativity pp. 289-320

Chapter 11. Predictions of General Relativity pp. 321-250

Notes pp. 351-354

References pp. 355-358

Index pp. 359-364

The book is written for senior students or first year graduate students of physics, applied mathematics, mathematics, astronomy and astrophysics who need a solid introduction to modern geometry and relativity. The book would also be of interest to non-specialists who would like a lucid introduction to this subject.

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