Основы математики и физики для подготовительного отделения

Description

Включает некоторые сведения по элементарной математике и основам дифференциального исчисления, а также основные разделы школьного курса физики — механику, молекулярную физику и термодинамику, электричество и магнетизм, оптику, атомную и ядерную физику. Предназначено для иностранных учащихся подготовительного отделения, обучающихся на английском языке. PREFACE THE BASICS OF ELEMENTARY MATHEMATICS AND DIFFERENTIAL CALCULUS 1. THE BASIC MATHEMATICAL CONCEPTS AND FORMULAS 1.1. FRACTION. OPERATIONS WITH FRACTIONS. EXPONENTS AND RADICALS. FACTORING AND EXPANDING 1.2. FUNCTIONAL DEPENDENCE. BASIC FUNCTIONS AND THEIR GRAPHS 1.3. VECTORS 1.4. ELEMENTARY GEOMETRY FIGURES AND FORMULAS 1.5. LIMIT OF A FUNCTION 1.6. DERIVATIVES AND INTEGRALS THE BASICS OF PHYSICS 2. KINEMATICS 2.1. MECHANICAL MOTION CHARACTERISTICS 2.2. UNIFORM LINEAR MOTION 2.3. NON-UNIFORM LINEAR MOTION 2.4. UNIFORMLY ACCELERATED LINEAR MOTION 2.5. FREELY FALLING OBJECTS 2.6. UNIFORM CIRCULAR MOTION 3. DYNAMICS 3.1. NEWTON’S LAWS OF MOTION 3.2. MAIN FORCES 3.3. CONSERVATION OF MOMENTUM 4. WORK. POWER. ENERGY 4.1. WORK 4.2. POWER 4.3. ENERGY 5. MECHANICAL OSCILLATIONS AND WAVES 5.1. MECHANICAL OSCILLATIONS 5.2. MECHANICAL WAVES 6. STATICS 6.1. CONDITIONS FOR EQUILIBRIUM 6.2. TYPES OF EQUILIBRIUM 6.3. CENTER OF MASS AND CENTER OF GRAVITATION 7. FLUID MECHANICS 7.1. DENSITY AND PRESSURE 7.2. PASCAL’S PRINCIPLE 7.3. ARCHIMEDES’ PRINCIPLE AND BUOYANCY 8. FUNDAMENTALS OF KINETIC THEORY OF GASES 8.1. ASSUMPTIONS OF KINETIC MOLECULAR THEORY OF GASES 8.2. AMOUNT OF SUBSTANCE, MOLAR MASS 8.3. IDEAL GAS. GAS PRESSURE 8.4. TEMPERATURE AS A MEASURE OF KINETIC ENERGY OF MOLECULES 8.5. IDEAL GAS LAW 8.6. ISOMETRIC PROCESSES 9. THERMAL PHENOMENA. BASICS OF THERMODYNAMICS 9.1. INTERNAL ENERGY. WORK OF GAS. FIRST LAW OF THERMODYNAMICS 9.2. FIRST LAW OF THERMODYNAMICS AT DIFFERENT PROCESSES 9.3. HEAT TRANSFER, TYPES OF HEAT TRANSFER 9.4. AMOUNT OF HEAT. SPECIFIC HEAT 9.5. PHASE CHANGES 9.6. THE HEAT BALANCE EQUATION 9.7. THERMAL EXPANSION. COEFFICIENT OF LINEAR AND VOLUME EXPANSION 10. ELECTRICITY 10.1. ELECTRIC CHARGE 10.2. LAW OF CONSERVATION OF ELECTRIC CHARGE 10.4. THE ELECTRIC FIELD. THE ELECTRIC FIELD STRENGTH 10.5. ELECTRIC POTENTIAL AND POTENTIAL DIFFERENCE 10.6. CAPACITORS. CAPACITANCE. ELECTRIC ENERGY STORAGE 10.7. THE EQUIVALENT CAPACITANCE 10.8. ENERGY STORED IN A CAPACITOR 10.9. AN ELECTRIC CURRENT 10.11. RESISTORS IN SERIES AND IN PARALLEL 10.12. ELECTRIC ENERGY AND ELECTRIC POWER 10.13. ELECTROMOTIVE FORCE. OHM’S LAW FOR A COMPLETE CIRCUIT 10.14. ALTERNATING CURRENT 11. MAGNETIC FIELD 11.1. THE MAGNETIC FIELD PRODUCED BY ELECTRIC CURRENT 11.2. FORCE ON AN ELECTRIC CURRENT IN A MAGNETIC FIELD (AMPERE’S FORCE) 11.3. FORCE ON AN ELECTRIC CHARGE MOVING IN A MAGNETIC FIELD (LORENTZ’S FORCE) 11.4. ELECTROMAGNETIC INDUCTION AND FARADAY’S LAW 11.5. FARADAY’S LAW OF INDUCTION 11.6. SELF-INDUCTANCE 11.7. MUTUAL INDUCTION 11.8. ENERGY STORED IN A MAGNETIC FIELD 11.9. LC CIRCUIT AND ELECTROMAGNETIC OSCILLATIONS 12. GEOMETRICAL OPTICS 12.1. THE RAY MODEL OF LIGHT 12.2. IMAGE FORMATION BY A FLAT MIRROR 12.3. REFRACTION. SNELL’S LAW 12.4. PHENOMENON OF TOTAL INTERNAL REFLECTION 12.5. THIN LENSES. RAY TRACING 12.6. THE THIN LENS EQUATION. MAGNIFICATION 13. THE WAVE NATURE OF LIGHT 13.1. ELECTROMAGNETIC WAVES SPECTRUM 13.2. LIGHT INTERFERENCE 13.3. DIFFRACTION OF LIGHT 13.4. DISPERSION OF LIGHT 13.5. QUANTUM PROPERTIES OF LIGHT. PHOTOELECTRIC EFFECT 14. ATOMIC PHYSICS 14.1. RUTHERFORD’S MODEL OF ATOM 14.2. BOHR’S THEORY OF THE HYDROGEN ATOM 14.3. ENERGY STATES OF A HYDROGEN ATOM 15. PHYSICS OF ATOMIC NUCLEUS 15.1. BINDING ENERGY 15.2. NUCLEAR REACTIONS 15.3. RADIOACTIVITY. ALPHA, BETA, AND GAMMA RADIATION 15.4. RADIOACTIVE DECAY LAW 15.5. NUCLEAR FISSION 15.6. ELEMENTARY PARTICLES REFERENCES Appendix CONTENTS