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E-raamat: General Relativity Without Calculus: A Concise Introduction to the Geometry of Relativity

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“General Relativity Without Calculus” offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physics. Targeted at first year undergraduates (and advanced high school students) who wish to learn Einstein’s theory beyond popular science accounts, it covers the basics of special relativity, Minkowski space-time, non-Euclidean geometry, Newtonian gravity, the Schwarzschild solution, black holes and cosmology. The quick-paced style is balanced by over 75 exercises (including full solutions), allowing readers to test and consolidate their understanding.

Requiring only basic knowledge of high school mathematics and physics, this volume offers a concise introduction to the general theory of relativity. The text presents the fundamentals of special relativity, Minkowski space-time, non-Euclidean geometry, Newtonian gravity, and more.

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From the reviews:

The book is a short, clear and elementary introduction to the main ideas of Special Relativity and General Relativity. The primary target was an audience of well-trained high school students, interested in a course beyond the popular science expositions. The contents reveals the aim of the author, to cover both the classic theory and the modern history of the Relativity Theory . (Gabriel Teodor Pripoae, Zentralblatt MATH, Vol. 1244, 2012)

1 Special Relativity
1(16)
1.1 Relativity of Motion
1(1)
1.2 Inertial Frames
2(1)
1.3 Galileo Transformations
3(1)
1.4 Velocity Addition Formula
4(1)
1.5 Lorentz Transformations
5(1)
1.6 Relativistic Velocity Addition Formula
6(1)
1.7 Time Dilation
7(1)
1.8 Derivation of the Lorentz Transformation Formulas
7(1)
1.9 Important Formulas
8(1)
1.10 Exercises
9(2)
1.11 Solutions
11(6)
2 Minkowski Geometry
17(18)
2.1 Units
17(1)
2.2 Space--Time Diagrams
18(1)
2.3 Interval Between Events
19(2)
2.4 Generalized Twin Paradox
21(3)
2.5 More Dimensions
24(1)
2.6 Important Formulas
25(1)
2.7 Exercises
25(3)
2.8 Solutions
28(7)
3 Non-Euclidean Geometry
35(14)
3.1 Curvilinear Coordinates
35(2)
3.2 The Sphere
37(2)
3.3 Geodesies
39(2)
3.4 Curvature
41(1)
3.5 Other Maps of the Sphere
42(2)
3.6 Other Geometries
44(1)
3.7 Exercises
45(1)
3.8 Solutions
46(3)
4 Gravity
49(10)
4.1 Newton's Law of Universal Gravitation
49(1)
4.2 Units
50(1)
4.3 Escape Velocity
50(1)
4.4 Kepler Laws
51(1)
4.5 Circular Orbits
52(2)
4.6 Important Formulas
54(1)
4.7 Exercises
54(1)
4.8 Solutions
55(4)
5 General Relativity
59(10)
5.1 Equivalence Principle
59(1)
5.2 Gravitational Redshift
60(1)
5.3 Curved Space--Time
61(2)
5.4 Important Formulas
63(1)
5.5 Exercises
64(1)
5.6 Solutions
65(4)
6 The Schwarzschild Solution
69(26)
6.1 The Schwarzschild Solution
70(1)
6.2 Stationary Observers
71(1)
6.3 Redshift
71(1)
6.4 Space Curvature
72(1)
6.5 Orbits
73(1)
6.6 Light Rays
74(3)
6.7 Black Holes
77(3)
6.8 Important Formulas
80(1)
6.9 Exercises
81(3)
6.10 Solutions
84(11)
7 Cosmology
95(20)
7.1 Redshift
95(1)
7.2 Hubble Law
96(1)
7.3 FLRW Models
96(3)
7.4 Hubble Law in the FLRW Models
99(1)
7.5 Redshift in the FLRW Models
100(1)
7.6 Friedmann Equations
101(2)
7.7 Important Formulas
103(1)
7.8 Exercises
104(2)
7.9 Solutions
106(9)
8 Mathematics and Physics
115(4)
8.1 Mathematics for General Relativity
115(1)
8.2 Modern Physics
116(3)
Astronomical Data 119(2)
Bibliography 121(2)
Index 123
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