| Foreword | |
| Preface | |
| Vector Calculus | |
| Introduction and Basic Definitions | |
| The Scalar Product | |
| Component Representation of a Vector | |
| The Vector Product (Axial Vector) | |
| The Triple Scalar Product | |
| Application of Vector Calculus Application in mathematics | |
| Application in physics | |
| Differentiation and Integration of Vectors | |
| The Moving Trihedral (Accompanying Dreibein)-the Frenet | |
| Formulas Examples on Frenet's formulas | |
| Surfaces in Space | |
| Coordinate Frames | |
| Vector Differential Operations | |
| The operations gradient, divergence, and curl (rotation) | |
| Differential operators in arbitrary general (curvilinear) coordinates | |
| Determination of Line Integrals | |
| The Integral Laws of Gauss and Stokes Gauss Law | |
| The Gauss theorem: Geometric interpretation of the Gauss theorem | |
| Stokes law | |
| Calculation of Surface Integrals | |
| Volume (Space) Integrals | |
| Newtonian Mechanics | |
| Newton's Axioms | |
| 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 | |
| The General Linear Motion | |
| The Free Fall Vertical throw | |
| Inclined throw | |
| Friction Friction phenomena in a viscous medium | |
| Motion in a viscous medium with | |
| Newtonian friction | |
| Generalized ansatz for friction | |
| The Harmonic Oscillator | |
| Mathematical Interlude-Series Expansion, Euler's Formulas | |
| The Damped Harmonic Oscillator | |
| The Pendulum | |
| Mathematical Interlude: Differential Equations | |
| Planetary Motions | |
| 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 | |
| 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? | |
| Theory Of Relativity | |
| Relativity Principle and Michelson-Morley Experiment | |
| The Michelson-Morley experiment | |
| The Lorentz Transformation | |
| Rotation of a three-dimensional coordinate frame | |
| The Minkowski space | |
| Group property of the | |
| Lorentz transformation | |
| 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 | |
| Addition Theorem of the Velocities | |
| Supervelocity of light, phase, and group velocity | |
| 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 | |
| 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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