A Mathematical Approach to Special Relativity introduces the mathematical formalisms of special and general relativity. Developed from the author’s experience teaching physics to students across all levels, the valuable resource introduces key concepts, building in complexity and using increasingly advanced mathematical tools as it progresses. Without assuming a background in calculus, the text begins with symmetry, before delving more deeply into Galilean relativity. Throughout, the book provides examples and useful "Guides to the Literature." This unique text emphasizes the experimental consequences and verifications of the underpinning theory in order to provide students with a solid foundation in this key area.
1. A Mathematical Approach to Special Relativity - p. Page i 2. Cover - p. Page i 3. Front Matter - p. Page i 4. Table of Contents - p. Page iii 5. Copyright - p. Page iii 6. Dedication - p. Page iv 7. Contents - p. Page vi 8. List of figures - p. Page vi 9. Biography - p. Page viii 10. Preface - p. Page ix 11. Acknowledgments - p. Page x 12. List of Illustrations - p. Page xii 13. Chapter 1 : Galilean relativity - p. Page xii 14. Chapter 2 : Failure of Newton's absolute time - p. Page 28 15. Chapter 3 : Lorentz boosts - p. Page 46 16. Chapter 4 : Development of the formalism - p. Page 73 17. Chapter 5 : Relativistic dynamics of particles - p. Page 89 18. Chapter 6 : Electrodynamics in covariant form - p. Page 115 19. Chapter 7 : Noninertial frames - p. Page 129 20. Chapter 8 : Gravity - p. Page 159 21. Chapter 9 : Mathematics of translations - p. Page 183 22. Chapter 10 : The rotation group - p. Page 197 23. Chapter 11 : The Lorentz group - p. Page 250 24. Appendix A : Elementary analytic geometry - p. Page 281 25. Appendix B : Active vs. passive rotations - p. Page 289 26. Appendix C : Projective (Möbius) action - p. Page 295 27. Appendix D : Metric, curvature, and geodesics of a surface - p. Page 301 28. Appendix E : Answers to selected problems - p. Page 312 29. Index - p. Page 324
A Mathematical Approach to Special Relativity introduces the mathematical formalisms of special and general relativity. Developed from the author’s experience teaching physics to students across all levels, the valuable resource introduces key concepts, building in complexity and using increasingly advanced mathematical tools as it progresses. Without assuming a background in calculus, the text begins with symmetry, before delving more deeply into Galilean relativity. Throughout, the book provides examples and useful "Guides to the Literature." This unique text emphasizes the experimental consequences and verifications of the underpinning theory in order to provide students with a solid foundation in this key area.
1. A Mathematical Approach to Special Relativity - p. Page i 2. Cover - p. Page i 3. Front Matter - p. Page i 4. Table of Contents - p. Page iii 5. Copyright - p. Page iii 6. Dedication - p. Page iv 7. Contents - p. Page vi 8. List of figures - p. Page vi 9. Biography - p. Page viii 10. Preface - p. Page ix 11. Acknowledgments - p. Page x 12. List of Illustrations - p. Page xii 13. Chapter 1 : Galilean relativity - p. Page xii 14. Chapter 2 : Failure of Newton's absolute time - p. Page 28 15. Chapter 3 : Lorentz boosts - p. Page 46 16. Chapter 4 : Development of the formalism - p. Page 73 17. Chapter 5 : Relativistic dynamics of particles - p. Page 89 18. Chapter 6 : Electrodynamics in covariant form - p. Page 115 19. Chapter 7 : Noninertial frames - p. Page 129 20. Chapter 8 : Gravity - p. Page 159 21. Chapter 9 : Mathematics of translations - p. Page 183 22. Chapter 10 : The rotation group - p. Page 197 23. Chapter 11 : The Lorentz group - p. Page 250 24. Appendix A : Elementary analytic geometry - p. Page 281 25. Appendix B : Active vs. passive rotations - p. Page 289 26. Appendix C : Projective (Möbius) action - p. Page 295 27. Appendix D : Metric, curvature, and geodesics of a surface - p. Page 301 28. Appendix E : Answers to selected problems - p. Page 312 29. Index - p. Page 324
