目錄
Foreword
Preface
I VECTOR CALCULUS
1 Introduction and Basic Definitions
2 The Scalar Product
3 Component Representation of a Vector
4 The Vector Product (Axial Vector)
5 The Triple Scalar Product
6 Application of Vector Calculus
Application in mathematics:
Application in physics:
7 Differentiation and Integration of Vectors
8 The Moving Trihedral (Accompanying Dreibein)--the Frenet Formulas
Examples on Frenet's formulas:
9 Surfaces in Space
10 Coordinate Frames
11 Vector Differential Operations
The operations gradient, divergence, and curl (rotation)
Differential operators in arbitrary general (curvilinear) coordinates
12 Determination of Line Integrals
13 The Integral Laws of Gauss and Stokes
Gauss Law:
The Gauss theorem:
Geometric interpretation of the Gauss theorem:
Stokes law:
14 Calculation of Surface Integrals
15 Volume (Space) Integrals
II NEWTONIAN MECHANICS
16 Newton's Axioms
17 Basic Concepts of Mechanics
Inertial systems
Measurement of masses
Work
Kinetic energy
Conservative forces
Potential
Energy law
Equivalence of impulse of force and momentum change
Angular momentum and torque
Conservation law of angular momentum
Law of conservation of the linear momentum
Summary
The law of areas
Conservation of orientation
18 The General Linear Motion
19 The Free Fall
Vertical throw
Inclined throw
20 Friction
Friction phenomena in a viscous medium
Motion in a viscous medium with Newtonian friction
Generalized ansatz for friction:
21 The Harmonic Oscillator
22 Mathematical Interlude--Series Expansion, Euler's Formulas
23 The Damped Harmonic Oscillator
24 The Pendulum
25 Mathematical Interlude: Differential Equations
26 Planetary Motions
27 Special Problems in Central Fields
The gravitational field of extended bodies
The attractive force of a spherical mass shell
The gravitational potential of a spherical shell covered with mass
Stability of circular orbits
28 The Earth and our Solar System
General notions of astronomy
Determination of astronomic quantities
Properties, position, and evolution of the solar system
World views
On the evolution of the universe
Dark Matter
What is the nature of the dark matter?
III THEORY OF RELATIVITY
29 Relativity Principle and Michelson-Morley Experiment
The Michelson-Morley experiment
30 The LorentzTransformation
Rotation of a three-dimensional coordinate frame
The Minkowski space
Group property of the Lorentz transformation
31 Properties of the Lorentz transformation
Time dilatation
Lorentz-Fitzgerald length contraction
Note on the invisibility of the Lorentz-Fitzgerald length contraction
The visible appearance of quickly moving bodies
Optical appearance of a quickly moving cube
Optical appearance of bodies moving with almost the speed of light
Light intensity distribution of a moving isotropic emitter
Doppler shift of quickly moving bodies
Relativistic space-time structure--space-time events
Relativistic past, present, future
The causality principle
The Lorentz transformation in the two-dimensional subspace of the Minkowski
space
32 Addition Theorem of the Velocities
Supervelocity of light, phase, and group velocity
33 The Basic Quantities of Mechanics in Minkowski Space
Lorentz scalars
Four-velocity in Minkowski space
Momentum in Minkowski space
Minkowski force (four-force)
Kinetic energy
The Tachyon hypothesis
Derivation of the energy law in the Minkowski space
The fourth momentum component
Conservation of momentum and energy for a free particle
Relativistic energy for free particles
Examples on the equivalence of mass and energy
34 Applications of the Special Theory of Relativity
The elastic collision
Compton scattering
The inelastic collision
Decay of an unstable particle
Index
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