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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