| SIMULATIONs | ............................................................................................................................................ | .. |
| 1) | 1) MEASUREMENT IN PHYSICS | |
| 2) | : 1 What does physics do? | |
| 3) | physical observables | |
| 3) | physical observables | |
| 3a) | nuclear dimensions | |
| 3b) | atomic dimensions | |
| 3c) | nanotechnology | |
| 3d) | microscopic objects | |
| 3e) | terrestrial dimensions | |
| 3f) | solar system size | |
| 3g) | galaxy size | |
| 3h) | universe dimensions | |
| 4) | the experimental method | |
| 5) | Galileo Galilei | |
| 6) | Physical law and mathematical language | |
| 7) | Physical Theories | |
| 8) | Physics and natural sciences | |
| 9) | Physics and technology | |
| 10) | 2 Physical quantities | |
| 11) | measurement of a physical quantity | |
| 12) | operational definition of physical quantities | |
| 13) | Correct expression of a measured physical quantity | |
| 14) | Multiple and sub-multiples of physical quantities | |
| 15) | Prefixes of physical quantities | |
| 16) | Fundamental quantities and derived quantities | |
| 17) | The physical dimensions of the quantities | |
| 18) | Physical dimension of a derived quantity | |
| 19) | 3 The international system and the fundamental dimensions of mechanics | |
| 20) | Absolute units of measure systems | |
| 21) | The International System | |
| 22) | Measure and unit of time | |
| 23) | Measurement and unit of lengths | |
| 24) | Measurement and unity of mass | |
| 25) | The radiant | |
| 26) | The steradian | |
| 27) | 4 Big numbers and small numbers | |
| 28) | Power properties | |
| 29) | Properties of powers of 10 | |
| 30) | The scientific notation | |
| 31) | Examples of time intervals | |
| 32) | Examples of lengths | |
| 33) | Examples of masses | |
| 34) | prefixes and powers of 10 | |
| 35) | Order of sizes | |
| 36) | 5 Direct and indirect measures | |
| 37) | Length measurements | |
| 38) | Area measurements | |
| 39) | Volume measurements | |
| 40) | The density | |
| 41) | Density measurement | |
| 42) | 6 Making estimates: Fermi's problems | |
| 43) | estimate of the order of magnitude | |
| 44) | examples of Fermi estimates | |
| 45) | 2) DATA PROCESSING IN PHYSICS | |
| 46) | : 1 Measurement errors | |
| 47) | 2 Estimate of the error | |
| 48) | 3 Error propagation and significant figures | |
| 49) | 4 The construction of a Cartesian graph | |
| 50) | 5 Representations of experimental data | |
| 51) | 6 Mathematical and graphic representation of physical laws | |
| 52) | 3) SCALAR SIZES AND VECTOR SIZES | |
| 53) | : 1 Displacement: a physical quantity to describe movement | |
| 54) | 2 Sum of trips | |
| 55) | 3 Scalars and vectors | |
| 56) | 4 Some operations on carriers | |
| 57) | 5 Decomposition of a carrier | |
| 58) | 6 Scalar product and vector product | |
| 59) | 4) FORCES AS VECTORS | |
| 60) | : 1 Forces | |
| 61) | 2 The weight force | |
| 62) | 3 Reaction to a deformation: the elastic force | |
| 63) | 4 The forces of constraint and friction | |
| 64) | 3 The weight force | |
| 65) | 5) THE BALANCE OF SOLIDS | |
| 66) | : 1 The balance of a material point | |
| 67) | 2 Moment of a force and a system of forces | |
| 68) | 3 The balance of a rigid body | |
| 69) | 4 Center of gravity and balance stability | |
| 70) | 5 Simple machines: levers and pulleys | |
| 71) | 6) PRESSURE AND BALANCE OF FLUIDS | |
| 72) | : 1 Fluids and pressure | |
| 73) | 2 Pressure in liquids | |
| 74) | 3 Atmospheric pressure | |
| 75) | 4 The flotation of bodies | |
| 76) | 7) THE UNIFORM MOTION | |
| 77) | : 1 The description of the motion | |
| 78) | 2 Speed | |
| 79) | 3 The space-time graph | |
| 80) | 4 The uniform rectilinear motion | |
| 81) | 8) THE UNIFORMLY ACCELERATED MOTION | |
| 82) | : 1 Acceleration | |
| 83) | 2 The speed-time graph | |
| 84) | 3 Uniformly accelerated motion | |
| 85) | 4 bodies in free fall | |
| 86) | 9) MOTIONS IN THE PLAN AND HARMONIC MOTION | |
| 87) | : 1 The motions in the plane | |
| 88) | 2 The motion of projectiles | |
| 89) | 3 Uniform circular motion | |
| 90) | 4 Displacement and angular velocity | |
| 91) | 5 Harmonic motion | |
| 92) | 10) THE NEWTONIAN DYNAMICS | |
| 93) | : 1 From the description of motion to its causes | |
| 94) | 2 The first principle of dynamics | |
| 95) | 3 The second principle of dynamics | |
| 96) | 4 The third principle of dynamics | |
| 97) | 5 Applications: falling motions | |
| 98) | 6 Applications: harmonic motion | |
| 99) | 11) WORK AND ENERGY | |
| 100) | : 1 The work of a constant force | |
| 101) | 2 The work of the weight force | |
| 102) | 3 The work of a variable force | |
| 103) | 4 The power | |
| 104) | 5 Kinetic energy | |
| 105) | 6 The potential energy | |
| 106) | 7 Energy conservation | |
| 107) | 12) TEMPERATURE AND HEAT | |
| 108) | : 1 Temperature and balance | |
| 109) | 2 Thermal expansion | |
| 110) | 3 Heat as energy in transit | |
| 111) | 4 Heat propagation | |
| 112) | 5 states of aggregation and status changes | |
| 113) | 13) GEOMETRIC OPTICS | |
| 114) | : 1) Light sources and light rays | |
| 115) | 2) Reflection | |
| 116) | 3) Refraction | |
| 117) | 4) Total reflection | |
| 118) | 5) Spherical mirrors | |
| 119) | 6) The lenses | |
| 120) | THREE-YEAR PERIOD | |
| 121) | : 1) THE LAWS OF DYNAMICS AND BALANCE | |
| 122) | : 1 The magnitudes of dynamics: a reminder | |
| 123) | 2 The Cartesian representation of vectors | |
| 124) | 3 Operations with vectors in Cartesian representation | |
| 125) | 4 Newton's laws | |
| 126) | 5 Equilibrium of the material point and of the rigid body | |
| 127) | 2) MOTIONS AS A RESULT OF THE LAWS OF DYNAMICS | |
| 128) | : 1 Uniform rectilinear motion | |
| 129) | 2 The accelerated uniform straight motion | |
| 130) | 3 The use of derivatives in physics: velocity and acceleration | |
| 131) | 4 Motion in two and three dimensions | |
| 132) | 5 Parabolic motion | |
| 133) | 6 Circular motion | |
| 134) | 7 The vector quantities of circular motion | |
| 135) | 8 Harmonic motion and the pendulum | |
| 136) | 3) INERTIAL AND NON-INERIAL REFERENCE SYSTEMS | |
| 137) | : 1 Classical composition of displacements, velocities and accelerations | |
| 138) | 2 The principle of classical relativity | |
| 139) | 3 Galilean transformations | |
| 140) | 4 Apparent forces in reference systems in accelerated translational motion | |
| 141) | 5 apparent forces in the reference systems in circular motion | |
| 142) | 4) MECHANICAL ENERGY | |
| 143) | : 1 Work as a scalar product | |
| 144) | 2 The work of a constant force: the case of weight force | |
| 145) | 3 The work of a variable force: the case of elastic force | |
| 146) | 4 Kinetic energy | |
| 147) | 5 Conservative forces and potential energy | |
| 148) | 6 Energy conservation | |
| 149) | 7 Average and instantaneous power | |
| 150) | 5) DYNAMICS OF FLUIDS | |
| 151) | : 1 Ideal fluids and real fluids | |
| 152) | 2 The continuity equation | |
| 153) | 3 The Bernoulli equation | |
| 154) | 4 The viscosity of fluids | |
| 155) | 6) THE QUANTITY OF MOTION AND IMPACT | |
| 156) | : 1 Amount of motion and impulse | |
| 157) | 2 The conservation of momentum | |
| 158) | 3 The bumps | |
| 159) | 4 Elastic collisions in one and two dimensions | |
| 160) | 5 Center of mass and motion of a particle system | |
| 161) | 7) ANGULAR MOMENT AND RIGID BODIES | |
| 162) | : 1 The angular momentum | |
| 163) | 2 The variation of the angular momentum | |
| 164) | 3 Moment of inertia and angular momentum of an extended body | |
| 165) | 4 Preservation of angular momentum http://web.tiscali.it/appunti.matematica/conservazion_esercizi_mix.pdf 5 The rotational dynamics of a rigid body | |
| 166) | 6 Kinetic energy, work and power in rotary motion | |
| 167) | 8) UNIVERSAL GRAVITATION | |
| 168) | : 1 The orbits of the planets | |
| 169) | 2 The law of universal gravitation | |
| 170) | 3 The gravitational field | |
| 171) | 4 The gravitational potential energy | |
| 172) | 5 Speed, period and energy of planets and satellites | |
| 173) | 9) GAS LAWS | |
| 174) | : 1 Temperature and thermometric scales | |
| 175) | 2 The gas laws | |
| 176) | 3 Boyle's law and the two laws of Gay-Lussac | |
| 177) | 4 The constant-volume gas thermometer and absolute zero | |
| 178) | 5 A simpler form for the laws of Gay-Lussac | |
| 179) | The equation of state of perfect gases | |
| 180) | 10) THE KINETIC THEORY OF GAS | |
| 181) | : 1 Molecular model of perfect gases | |
| 182) | 2 Molecular shocks and pressure | |
| 183) | 3 Average quadratic speed and temperature | |
| 184) | 4 The Maxwell distribution | |
| 185) | 5 The average kinetic energy | |
| 186) | 6 The properties of real gases | |
| 187) | 11) The first principle of dynamics | |
| 188) | : 1 Heat, thermal equilibrium and state changes | |
| 189) | 2 Heat propagation | |
| 190) | 3 Thermodynamic systems and transformations | |
| 191) | 4 Thermodynamic work | |
| 192) | 5 The first principle: energy conservation | |
| 193) | 6 Internal energy and specific heats of a perfect gas | |
| 194) | 7 The first principle and adiabatic transformations | |
| 195) | 12) SECOND PRINCIPLE OF THERMODYNAMICS AND ENTROPY | |
| 196) | : 1 Thermal machines | |
| 197) | 2 The second principle: the privileged verse | |
| 198) | 3 The Carnot cycle and the maximum efficiency of thermal machines | |
| 199) | 4 Refrigerating machines | |
| 200) | 5 The entropy of Clausius | |
| 201) | 6 The second principle is a principle of "non conservation" | |
| 202) | 7 Entropy and disorder: the Boltzmann equation | |
| 203) | 13) THE PROPERTIES OF THE WAVING MOTORS | |
| 204) | : 1 The undulatory motions | |
| 205) | 2 The wave function | |
| 206) | 3 The overlapping principle: interference | |
| 207) | 4 The beats | |
| 208) | 5 Reflection and standing waves | |
| 209) | 6 Wave diffraction and the Huygens principle | |
| 210) | 14) SOUND | |
| 211) | : 1 Sources and propagation of sound waves | |
| 212) | 2 The characteristics of sound | |
| 213) | 3 The perception of sound | |
| 214) | 4 The Doppler effect | |
| 215) | 15) THE WAVY PROPERTIES OF LIGHT | |
| 216) | : 1 The refraction of light | |
| 217) | 2 Light interference | |
| 218) | 3 Interference on a thin layer | |
| 219) | 4 Young's double slit interferometer | |
| 220) | 5 The diffraction of light | |
| 221) | 6 The polarization of light | |
| 222) | 7 Energy transported by light | |
| 223) | 16) THE ELECTRIC CHARGE AND THE LAW OF COULOMB | |
| 224) | : 1 The electric charge and the interactions between electrified bodies | |
| 225) | 2 Conductors and insulators. Contact electrification | |
| 226) | 3 Electrostatic induction | |
| 227) | 4 The polarization of dielectrics | |
| 228) | 5 The law of Coulomb | |
| 229) | 17) THE ELECTRIC FIELD | |
| 230) | : 1 The concept of the electric field | |
| 231) | 2 The electric field generated by point charges | |
| 232) | 3 The flow of the electric field and the Gauss theorem | |
| 233) | 4 Applications of the Gauss theorem | |
| 234) | 18) POTENTIAL AND CAPACITY | |
| 235) | : 1 The potential electric energy | |
| 236) | 2 The electric potential and the potential difference | |
| 237) | 3 The electric field circuitry | |
| 238) | 4 The potential of a conductor in electrostatic equilibrium | |
| 239) | 5 Capacitors and capacitance | |
| 240) | 6 Capacitor systems | |
| 241) | 7 The accumulation of electricity in a capacitor | |
| 242) | 19) THE ELECTRICITY AND THE OHM LAWS | |
| 243) | : 1 The electric current | |
| 244) | 2 Electric resistance and Ohm's first law | |
| 245) | 3 The second law of Ohm | |
| 246) | 4 Microscopic interpretation of Ohm's laws | |
| 247) | 20) ELECTRICAL CIRCUITS | |
| 248) | : 1 The electromotive force | |
| 249) | 2 Direct current electrical circuits: Kirchhoof's laws | |
| 250) | 3 Resistance systems | |
| 251) | 4 RC circuits | |
| 252) | 5 Electric power | |
| 253) | 6 Instruments for electrical quantities | |
| 254) | 7 The extraction of electrons from a metal | |
| 255) | 21) THE ELECTRIC CURRENT IN THE FLUIDS AND THE VACUUM | |
| 256) | : 1 Batteries and accumulators | |
| 257) | 2 Electrolytic solutions and electrolysis | |
| 258) | 3 Faraday's laws | |
| 259) | 4 Electrical conduction in gases | |
| 260) | 5 Electric currents through the vacuum | |
| 261) | 22) THE MAGNETISM | |
| 262) | : 1 The magnets and the electric field | |
| 263) | 2 The magnetic induction | |
| 264) | 3 The magnetic fields generated by currents | |
| 265) | 4 The flow and circulation of the magnetic field | |
| 266) | 5 Magnetic forces on currents | |
| 267) | 6 The magnetic force on a moving electric charge | |
| 268) | 7 The action of a magnetic field on a loop covered by current | |
| 269) | 8 The magnetic properties of matter | |
| 270) | 23) CHARGES IN ELECTRIC AND MAGNETIC FIELDS | |
| 271) | : 1 The motion of a charge in an electric field | |
| 272) | 2 Applications: Millikan's experiment | |
| 273) | 3 The motion of a charge in a magnetic field | |
| 274) | 4 Applications: Thomson's experiment | |
| 275) | 5 Applications: the mass spectrograph | |
| 276) | 6 Applications: the Hall effect | |
| 277) | 24) ELECTROMAGNETIC INDUCTION | |
| 278) | : 1 Induced current | |
| 279) | 2 Faraday-Neumann's law and Lenz's law | |
| 280) | 3 Mutual induction and self-induction | |
| 281) | 4 RL Circuits and inductor energy | |
| 282) | 25) THE ALTERNATING CURRENT | |
| 283) | : 1 The alternator | |
| 284) | 2 Electric circuits in alternating current | |
| 285) | 3 The RLC circuit | |
| 286) | 4 The power absorbed by a circuit | |
| 287) | 5 The transformer | |
| 288) | 26) ELECTROMAGNETIC WAVES | |
| 289) | : 1 The electromagnetic field and the speed of light | |
| 290) | 2 The displacement current | |
| 291) | 3 Maxwell's equations | |
| 292) | 4 The propagation of electromagnetic waves | |
| 293) | 5 The energy and momentum transported by an electromagnetic wave | |
| 294) | 6 Production and reception of electromagnetic waves | |
| 295) | 7 The electromagnetic spectrum | |
| 296) | 27) KINEMATICS IN RESTRICTED RELATIVITY | |
| 297) | : 1 The crisis of the principle of classical relativity | |
| 298) | 2 The postulates of special relativity | |
| 299) | 3 Lorentz transformations | |
| 300) | 4 A new concept of simultaneity | |
| 301) | 5 Time dilation | |
| 302) | 6 The contraction of lengths | |
| 303) | 7 Relativistic composition of velocities | |
| 304) | 8 Space time | |
| 305) | 28) RELATIVIST DYNAMICS AND GENERAL RELATIVITY | |
| 306) | : 1 Mass and quantity of motion in the relativistic dynamics | |
| 307) | 2 Mass-energy equivalence | |
| 308) | 3 General relativity: a new principle of equivalence | |
| 309) | 4 Gravity and the curvature of space-time | |
| 310) | 5 Experimental verifications of general relativity | |
| 311) | 6 Gravitational wave research | |
| 312) | 29) ORIGINS OF PHYSICS OF THOSE | |
| 313) | : 1 Black-body radiation and Planck quanta | |
| 314) | 2 The light quanta and the photoelectric effect | |
| 315) | 3 The Compton effect | |
| 316) | 4 The characteristic spectra of atoms | |
| 317) | 5 The first atomic models | |
| 318) | 6 The Bohr model | |
| 319) | 7 Quantized orbits and spectral lines of atoms | |
| 320) | 30) WAVES, BODIES AND INDETERMINATION | |
| 321) | : 1 The wave-corpuscle duality | |
| 322) | 2 Wave mechanics | |
| 323) | 3 The quantum numbers of the hydrogen atom | |
| 324) | 4 The electronic configuration of complex atoms | |
| 325) | 5 The Heisenberg uncertainty principle | |
| 326) | 6 The Tunnel effect | |
| 327) | 31.A) THE PHYSICS OF THE SOLID STATE | |
| 328) | : 1 The molecules and crystalline solids | |
| 329) | 2 The energy band theory | |
| 330) | 3 The doping of semiconductors | |
| 331) | 4 The pn junction | |
| 332) | 5 Transistors and integrated circuits | |
| 333) | 6 Superconductivity | |
| 334) | 31.B) THE NUCLEUS AND RADIOACTIVITY | |
| 335) | : 1 The structure of the atomic nucleus | |
| 336) | 2 Natural radioactivity | |
| 337) | 3 Radioactive decay | |
| 338) | 4 The biological effects of ionizing radiation | |
| 339) | 5 Artificial transmutations and synthetic elements | |
| 340) | 6 Nuclear fission | |
| 341) | 7 Nuclear fusion | |
| 342) | 31.C) THE ELEMENTARY PARTICLES AND THEIR INTERACTIONS | |
| 343) | : 1 The ultimate constituents of the subject | |
| 344) | 2 The neutrinos | |
| 345) | 3 Conservation laws and quantum numbers in particle physics | |
| 346) | 4 The charm of quarks | |
| 347) | 5 The Standard Model and the frontiers of physics | |
| 348) | 31.D) ASTROPHYSICS AND COSMOLOGY | |
| 349) | : 1 The Sun, the stars and the galaxies | |
| 350) | 2 Stellar evolution: birth, life and death of the stars | |
| 351) | 3 Radio astronomy and the mysterious objects of distant galaxies | |
| 352) | 4 The expanding universe | |
| 353) | 5 The Big Bang hypothesis | |
| 354) | 6 The future of the universe | |
| 355) | 1 La struttura del nucleo atomico | |
| 356) | MATHEMATICS | |
| 357) | : FIRST YEAR | |
| 358) | : 1) NATURAL NUMBERS | |
| 359) | : 1 What are natural numbers | |
| 360) | 2 The four operations | |
| 361) | 3 The powers | |
| 362) | 4 Expressions with natural numbers | |
| 363) | 5 The properties of operations | |
| 364) | 6 The properties of powers | |
| 365) | 7 The multiples and divisors of a number | |
| 366) | 8 The greatest common divisor is the common minimum | |
| 367) | 9 Numbering systems | |
| 368) | 2) INTERNAL NUMBERS: | |
| 369) | 1 What are integers | |
| 370) | 2 Addition and subtraction | |
| 371) | 3 Multiplication, division and power | |
| 372) | 4 The laws of monotony | |
| 373) | 3) RATIONAL NUMBERS AND REAL NUMBERS: | |
| 374) | 1 From fractions to rational numbers | |
| 375) | 2 The comparison of rational numbers | |
| 376) | 3 Operations in Q | |
| 377) | 4 Powers with negative integer exponent | |
| 378) | 5 Rational numbers and decimal numbers | |
| 379) | 6 The real numbers | |
| 380) | 7 Fractions and proportions | |
| 381) | 8 Percentages | |
| 382) | 9 The approximate calculation | |
| 383) | 10 The scientific notation and the order of magnitude | |
| 384) | 4) THE SETS AND THE LOGIC: | |
| 385) | 1 What is a whole | |
| 386) | 2 The representations of a whole | |
| 387) | 3 The subsets | |
| 388) | 4 Operations with sets | |
| 389) | 5 The set of parts and the partition of a set | |
| 390) | 6 The logical propositions | |
| 391) | 7 Logical connectives and expressions | |
| 392) | 8 Valid forms of reasoning | |
| 393) | 9 Logic and sets | |
| 394) | 10 The quantifiers | |
| 395) | 5) RELATIONS AND FUNCTIONS: | |
| 396) | 1 Binary relations | |
| 397) | 2 The relationships defined in a whole and their properties | |
| 398) | 3 Equivalence relations | |
| 399) | 4 Ordering reports | |
| 400) | 5 The functions | |
| 401) | 6 Numerical functions | |
| 402) | 7 The Cartesian plane and the graph of a function | |
| 403) | 8 Special numerical functions | |
| 404) | 9 The circular functions | |
| 405) | 6) THE MONOMES: | |
| 406) | 1 What are monomials | |
| 407) | 2 Operations with monomials | |
| 408) | 3 Maximum common divisor and least common multiple of monomials | |
| 409) | 7) PYRINOMICS: | |
| 410) | 1 What are polynomials | |
| 411) | 2 Operations with polynomials | |
| 412) | 3 Notable products | |
| 413) | 4 Polynomial functions | |
| 414) | 5 The division between polynomials | |
| 415) | 6 Ruffini's rule | |
| 416) | 7 The theorem of the rest | |
| 417) | 8 Ruffini's theorem | |
| 418) | 8) BREAKDOWN IN FACTORS: | |
| 419) | 1 Factor decomposition of polynomials Summary: Polynomial decomposition | |
| 420) | 2 The MCD and the mcm between polynomials | |
| 421) | 9) ALGEBRIC FRACTIONS: | |
| 422) | 1 Algebraic fractions | |
| 423) | 2 The calculation with algebraic fractions | |
| 424) | 10) LINEAR EQUATIONS: | |
| 425) | 1 Identities | |
| 426) | 2 The equations | |
| 427) | 3 The principles of equivalence | |
| 428) | 4 The whole numerical equations | |
| 429) | 5 Equations and problems | |
| 430) | 6 The fractional equations | |
| 431) | 7 Literal equations | |
| 432) | 11) LINEAR DISEQUATIONS: | |
| 433) | 1 Numerical inequalities Inequalities | |
| 434) | 2 The whole inequalities | |
| 435) | 3 The systems of inequalities | |
| 436) | 4 Equations with absolute values | |
| 437) | 5 Inequalities with absolute values The study of the sign of a product | |
| 438) | 6 Fractional inequalities | |
| 439) | 12) ELEMENTS OF COMPUTER SCIENCE: | |
| 440) | 1 Numbers and digital information | |
| 441) | 2 Problems and algorithms | |
| 442) | 3 Program with Python | |
| 443) | 13) INTRODUCTION TO THE STATISTICS: | |
| 444) | 1 Statistical data | |
| 445) | 2 The graphical representation of the data | |
| 446) | 3 The central position indices | |
| 447) | 4 Variability indices | |
| 448) | G1) THE GEOMETRY OF THE PLAN: | |
| 449) | 1 Geometrical objects and properties | |
| 450) | 2 The postulates of belonging and order | |
| 451) | 3 The fundamental bodies | |
| 452) | 4 Operations with segments and angles Figures and demonstrations | |
| 453) | 5 Lengths, widths, measures | |
| 454) | G2) THE TRIANGLES: | |
| 455) | 1 First definitions on triangles | |
| 456) | 2 The first criterion of congruence | |
| 457) | 3 The second criterion of congruence | |
| 458) | 4 The properties of the isosceles triangle | |
| 459) | 5 The third criterion of congruence; Congruence criteria and isosceles and equilateral triangles | |
| 460) | 6 Inequalities in triangles | |
| 461) | G3) PERPENDICULAR AND PARALLEL: | |
| 462) | 1 The perpendicular lines | |
| 463) | 2 The parallel lines | |
| 464) | 3 The properties of polygon angles | |
| 465) | 4 The criteria of congruence of the right-angled triangles | |
| 466) | G4) PARALLELOGRAMS AND TRAPEZIES: | |
| 467) | 1 The parallelogram | |
| 468) | 2 The rectangle | |
| 469) | 3 The turbot | |
| 470) | 4 The square | |
| 471) | 5 The trapeze | |
| 472) | 6 The correspondences in a bundle of parallel lines | |
| 473) | SECOND YEAR | |
| 474) | : 13) LINEAR SYSTEMS: | |
| 475) | 1 The systems of two equations in two unknowns | |
| 476) | 2 The replacement method | |
| 477) | 3 Determined, impossible, indeterminate systems | |
| 478) | 4 The comparison method | |
| 479) | 5 The reduction method | |
| 480) | 6 The matrices and determinants | |
| 481) | 7 The Cramer method | |
| 482) | 8 The systems of three equations in three unknowns | |
| 483) | 9 The literal and fract systems | |
| 484) | 10 Linear systems and problems | |
| 485) | 14) THE RADICALS: | |
| 486) | 1 Real numbers | |
| 487) | 2 Square roots and cubic roots | |
| 488) | 3 The nth root | |
| 489) | 4 Simplification and comparison of radicals | |
| 490) | 15) OPERATIONS WITH RADICALS: | |
| 491) | 1 Multiplication and division of roots | |
| 492) | 2 The transport of a factor outside or inside the root sign | |
| 493) | 3 The power and root of a radical | |
| 494) | 4 Addition and subtraction of radicals | |
| 495) | 5 The rationalization of the denominator of a fraction | |
| 496) | 16) THE CARTESIAN PLAN AND THE RIGHT: | |
| 497) | 1 Points and segments | |
| 498) | 2 The distance between two points is the midpoint | |
| 499) | 3 The equation of a line passing through the origin | |
| 500) | 4 The general equation of the line | |
| 501) | 5 The straight lines and the linear systems | |
| 502) | 6 Parallel lines and perpendicular lines | |
| 503) | 7 The bundles of lines | |
| 504) | 8 How to determine the equation of a line | |
| 505) | 9 The distance of a point from a line | |
| 506) | 10 The parts of the plan and the line | |
| 507) | 17) THE SECOND-GRADE EQUATIONS AND THE PARABOLA: | |
| 508) | 1 The second degree equations: definitions | |
| 509) | 2 The resolution of a second degree equation | |
| 510) | 3 The whole numerical equations | |
| 511) | 4 The quadratic function and the parabola | |
| 512) | 5 The relations between the roots and the coefficients | |
| 513) | 6 The rule of Descartes | |
| 514) | 7 The decomposition of a second degree trinomial | |
| 515) | 8 Secondary equations and problems | |
| 516) | 18) THE APPLICATIONS OF SECOND-GRADE EQUATIONS: | |
| 517) | 1 The fractional and literal equations | |
| 518) | 2 Equations and problems | |
| 519) | 3 The second degree parametric equations | |
| 520) | 4 Equations higher than the second degree | |
| 521) | 19) SECOND DEGREE SYSTEMS AND UPPER DEGREE: | |
| 522) | 1 The second degree systems | |
| 523) | 2 The graphic interpretation of second degree systems | |
| 524) | 3 Systems higher than the second degree | |
| 525) | 4 Problems with higher than second degree systems | |
| 526) | 20) THE SECOND-DEGREE DISEQUATIONS AND UPPER DEGREE: | |
| 527) | 1 Linear inequalities | |
| 528) | 2 The sign of entire second degree inequalities | |
| 529) | 3 The resolution of entire second degree inequalities | |
| 530) | 4 The whole inequalities of degree higher than the second | |
| 531) | 5 The broken inequalities | |
| 532) | 6 The systems of inequalities | |
| 533) | 7 Problems with inequalities | |
| 534) | 21) APPLICATIONS OF DISEQUATIONS: | |
| 535) | 1 Parametric equations | |
| 536) | 2 The irrational equations | |
| 537) | 3 Irrational inequalities | |
| 538) | 4 Equations with absolute values | |
| 539) | 5 Inequalities with absolute values | |
| 540) | 6 Function graphs with absolute values | |
| 541) | Beta) INTRODUCTION TO PROBABILITY: | |
| 542) | 1 Events and the sample space | |
| 543) | 2 The classical definition of probability | |
| 544) | 3 Operations with events | |
| 545) | 4 Theorems related to probability calculus | |
| 546) | 5 Other definitions of probability | |
| 547) | G5) THE CIRCUMFERENCE: | |
| 548) | 1 The geometric places | |
| 549) | 2 The circumference and the circle | |
| 550) | 3 Theorems on the strings | |
| 551) | 4 Circumferences and lines | |
| 552) | 5 The mutual positions between two circles | |
| 553) | 6 The angles on the circumference | |
| 554) | G6) THE INSCRIBED AND CIRCUMSCRIBED POLIGONES: | |
| 555) | 1 The inscribed polygons | |
| 556) | 2 The circumscribed polygons | |
| 557) | 3 The triangles and the remarkable points | |
| 558) | 4 The quadrilaterals inscribed and circumscribed | |
| 559) | 5 The regular polygons | |
| 560) | G7) EQUIVALENT SURFACES AND AREAS: | |
| 561) | 1 The equivalence of surfaces | |
| 562) | 2 The equivalence of parallelograms | |
| 563) | 3 Triangles and equivalence | |
| 564) | 4 The equivalence between a circumscribed polygon and a triangle | |
| 565) | 5 The construction of equivalent polygons | |
| 566) | 6 Measurement of polygon areas | |
| 567) | G8) THE THEOREMES OF EUCLIDE AND PITAGORA: | |
| 568) | 1 Euclid's first theorem | |
| 569) | 2 The Pythagorean theorem | |
| 570) | 3 Applications of the Pythagorean theorem | |
| 571) | 4 Euclid's second theorem | |
| 572) | G9) PROPORTIONALITY: | |
| 573) | 1 Geometric quantities | |
| 574) | 2 The commensurable and incommensurable magnitudes | |
| 575) | G10) THE SIMILITUDE: | |
| 576) | 1 The simile and the triangles | |
| 577) | 2 The triangularity similarity criteria | |
| 578) | 3 The simile and the theorems of Euclid | |
| 579) | 4 Similarity and polygons | |
| 580) | 5 Similarity and circumference | |
| 581) | 6 The golden section and its applications | |
| 582) | 7 The length of the circumference and the area of the circle | |
| 583) | G11) GEOMETRIC TRANSFORMATIONS: | |
| 584) | 1 Geometric transformations and isometries | |
| 585) | 2 Translation | |
| 586) | 3 The rotation | |
| 587) | 4 The central symmetry | |
| 588) | 5 Axial symmetry | |
| 589) | 6 A non-isometric transformation: the homothetic | |
| 590) | THIRD YEAR | |
| 591) | : 1) EQUATIONS AND DISEQUATIONS: | |
| 592) | 1 Inequalities and principles of equivalence | |
| 593) | 2 First-degree inequalities | |
| 594) | 3 Second Degree Inequalities | |
| 595) | 4 Full second inequalities | |
| 596) | 5 Inequalities of a grade higher than the second | |
| 597) | 6 Fractional inequalities | |
| 598) | 7 Systems of inequalities | |
| 599) | 8 Equations and inequalities with absolute values | |
| 600) | 9 Irrational equations and inequalities | |
| 601) | 2) FUNCTIONS: | |
| 602) | 1 Functions and their characteristics | |
| 603) | 2 Injective, surjective and bijective functions | |
| 604) | 3 Inverse function | |
| 605) | 4 Properties of the functions | |
| 606) | 5 Compound functions | |
| 607) | 6 Geometric and graphic transformations | |
| 608) | 3) SUCCESSIONS AND PROGRESSIONS: | |
| 609) | 1 Numerical sequences | |
| 610) | 2 Induction principle | |
| 611) | 3 Arithmetic progressions | |
| 612) | 4 Geometric progressions | |
| 613) | 4) CARTESIAN AND STRAIGHT PLAN: | |
| 614) | 1 Coordinates in the plan | |
| 615) | 2 Length of a segment | |
| 616) | 3 Midpoint of a segment, center of gravity of a triangle | |
| 617) | 4 Parallel lines and perpendicular lines | |
| 618) | 5 Distance of a point from a line | |
| 619) | 6 Geometric and straight places | |
| 620) | 7 Bundles of lines | |
| 621) | 8 Problems with straight lines | |
| 622) | 5) PARABOLA: | |
| 623) | 1 Parable and its equation | |
| 624) | 2 Parabola with axis parallel to the axis x Parabola and functions | |
| 625) | 3 Parabola and geometric transformations | |
| 626) | 4 Lines and parabolas | |
| 627) | 5 Determine the equation of a parabola | |
| 628) | 6 Search for the equation of a parabola | |
| 629) | 7 Bundles of parabolas | |
| 630) | 6) CIRCUMFERENCE: | |
| 631) | 1 Circumference and its equation | |
| 632) | 2 Lines and circumferences | |
| 633) | 3 Determine the equation of a circle | |
| 634) | 4 Position of two circles | |
| 635) | 5 Bundles of circumferences | |
| 636) | 7) ELLIPSE: | |
| 637) | 1 Ellipse and its equation | |
| 638) | 2 Ellipses and lines | |
| 639) | 3 Determine the equation of an ellipse | |
| 640) | 4 Ellipse and geometric transformations | |
| 641) | 8) HYPERBOLE: | |
| 642) | 1 Hyperbole and its equation | |
| 643) | 2 Hyperbolas and lines | |
| 644) | 3 Determine the equation of a hyperbola | |
| 645) | 4 Hyperbola translated | |
| 646) | 5 Equilateral hyperbole | |
| 647) | 9) CONIC: | |
| 648) | 1 Definition of a conic by eccentricity | |
| 649) | 2 Second degree inequalities in two unknowns | |
| 650) | 3 Conics and geometric problems | |
| 651) | FOURTH YEAR | |
| 652) | : 10) EXPONENTIALS: | |
| 653) | 1 Powers with real exponent | |
| 654) | 2 Exponential function | |
| 655) | 3 Exponential equations | |
| 656) | 4 Exponential inequalities | |
| 657) | 11) LOGARITMI: | |
| 658) | 1 Definition of logarithm | |
| 659) | 2 Logarithm properties | |
| 660) | 3 Logarithmic function | |
| 661) | 4 Logarithmic equations | |
| 662) | 5 Logarithmic equations | |
| 663) | 6 Logarithmic inequalities | |
| 664) | 7 Logarithmic inequalities | |
| 665) | 8 Logarithms and exponential equations and inequalities | |
| 666) | 9 Domain and sign of functions with exponentials and logarithms | |
| 667) | 10 Logarithmic equations and inequalities that can be solved only graphically | |
| 668) | 11 Logarithmic and semilogarithmic coordinates | |
| 669) | BETA_1) UNIQUE STATISTICS: | |
| 670) | 1 Statistical data | |
| 671) | 2 Indices of position and variability | |
| 672) | 3 Gaussian distribution | |
| 673) | 4 Statistical reports | |
| 674) | 5 Effectiveness, efficiency, quality | |
| 675) | 6 Indicators of effectiveness, efficiency, quality | |
| 676) | 7 Reports and indicators | |
| 677) | BETA_2) BIVARIATE STATISTICS: | |
| 678) | 1 Introduction to bivariate statistics | |
| 679) | 2 Regression | |
| 680) | 3 Correlation | |
| 681) | C1) POLAR COORDINATES IN THE PLAN: | |
| 682) | 1 Polar coordinates | |
| 683) | 2 Curve equations | |
| 684) | 3 Uniform circular motion | |
| 685) | C2) APPROXIMATE CALCULATION: | |
| 686) | 1 The approximations | |
| 687) | 2 Error propagation | |
| 688) | C3) CARRIERS: | |
| 689) | 1 Vectors in the plan | |
| 690) | 2 Linearly dependent and independent vectors | |
| 691) | 3 Scalar product and vector product | |
| 692) | 4 Cartesian representation of vectors | |
| 693) | C4) MATRICES AND DETERMINANTS: | |
| 694) | 1 Matrices | |
| 695) | 2 Square matrices | |
| 696) | 3 Operations with matrices | |
| 697) | 4 Determinants | |
| 698) | 5 Properties of determinants | |
| 699) | 6 Rank | |
| 700) | 7 Reverse matrix | |
| 701) | 8 Some applications of matrices and determinants | |
| 702) | C5) LINEAR EQUATION SYSTEMS: | |
| 703) | 1 What are linear systems | |
| 704) | 2 Inverse matrix method | |
| 705) | 3 Cramer's rule | |
| 706) | 4 Reduction method | |
| 707) | 5 Theorem of Rouché - Capelli | |
| 708) | 6 Homogeneous linear systems of n equations in n unknowns | |
| 709) | C6) CONICAL SECTIONS: THE SYNTHETIC POINT OF VIEW: | |
| 710) | 1 The Dandelin theorems | |
| 711) | 2 The parabolic segment | |
| 712) | C7) SPEED OF VARIATION OF A GREATNESS: | |
| 713) | 1 Average speed and instantaneous variation | |
| 714) | 12) GONIOMETRIC FUNCTIONS: | |
| 715) | 1 Angle measurement | |
| 716) | 2 Sine and cosine functions | |
| 717) | 3 Tangent function | |
| 718) | 4 Secant and cosecant functions | |
| 719) | 5 Cotangent function | |
| 720) | 6 Goniometric functions of particular angles | |
| 721) | 7 Associated corners | |
| 722) | 8 Inverse goniometric functions | |
| 723) | 9 Goniometric functions and geometric transformations | |
| 724) | 13) GONIOMETRIC FORMULAS: | |
| 725) | 1 Addition and subtraction formulas | |
| 726) | 2 Duplication formulas | |
| 727) | 3 Bisection formulas | |
| 728) | 4 Parametric formulas | |
| 729) | 5 Prosthesis and Werner formulas | |
| 730) | 14) GONIOMETRIC EQUATIONS AND DISEQUATIONS: | |
| 731) | 1 Elementary goniometric equations | |
| 732) | 2 Linear equations in sine and cosine | |
| 733) | 3 Homogeneous second degree equations in the sine and cosine | |
| 734) | 4 Systems of goniometric equations | |
| 735) | 5 Goniometric inequalities | |
| 736) | 15) TRIGONOMETRY: | |
| 737) | 1 Rectangular triangles | |
| 738) | 2 Applications of theorems on right-angled triangles | |
| 739) | 3 Triangles any | |
| 740) | 4 Applications to trigonometry | |
| 741) | 5 Cosine theorem | |
| 742) | 16) COMPLEX NUMBERS: | |
| 743) | 1 Algebraic form of complex numbers | |
| 744) | 2 Operations with imaginary numbers | |
| 745) | 3 Operations with complex numbers in algebraic form | |
| 746) | 4 Algebraic representation of complex numbers | |
| 747) | 5 Trigonometric form of a complex number | |
| 748) | 6 Operations between complex numbers in trigonometric form | |
| 749) | 7 Nth roots of the unit | |
| 750) | 17) CARRIERS, MATRICES, DETERMINANTS: | |
| 751) | 1 Vectors in the plan | |
| 752) | 2 Vectors in the Cartesian plane | |
| 753) | 3 Matrices | |
| 754) | 4 Operations with matrices | |
| 755) | 5 Determinants | |
| 756) | 6 Reverse matrix | |
| 757) | 7 Matrices and analytical geometry | |
| 758) | 18) GEOMETRIC TRANSFORMATIONS: | |
| 759) | 1 Translation | |
| 760) | 2 Rotation | |
| 761) | 3 Central symmetry | |
| 762) | 4 Axial symmetry | |
| 763) | 5 Isometries | |
| 764) | 6 Omotetia | |
| 765) | 7 Similarity | |
| 766) | 8 Affinity | |
| 767) | 19) EUCLIDEA GEOMETRY IN SPACE: | |
| 768) | 1 Points, lines, planes in space | |
| 769) | 2 Perpendicularity and parallelism | |
| 770) | 3 Distances and angles in space | |
| 771) | 4 Geometric transformations | |
| 772) | 5 Polyhedra | |
| 773) | 6 Rotating solids | |
| 774) | 7 Solids areas | |
| 775) | 8 Extension and equivalence of solids | |
| 776) | 9 Volumes of solids | |
| 777) | 20) ANALYTICAL GEOMETRY IN THE SPACE: | |
| 778) | 1 Coordinates in space | |
| 779) | 2 Vectors in space | |
| 780) | 3 Plan and its equation | |
| 781) | 4 Line and its equation | |
| 782) | 5 Mutual position of a line and a plane | |
| 783) | 6 Some notable surfaces | |
| 784) | Alfa1) COMBINATORIAL CALCULATION: | |
| 785) | 1 What is combinatorial calculus | |
| 786) | 2 Provisions | |
| 787) | 3 Permutations | |
| 788) | 4 Combinations | |
| 789) | 5 Newton's binomial | |
| 790) | Alfa2) PROBABILITY: | |
| 791) | 1 Events | |
| 792) | 2 Classical concept of probability | |
| 793) | 3 Logical sum of events | |
| 794) | 4 Conditional probability | |
| 795) | 5 Logical product of events | |
| 796) | 6 Bayes theorem | |
| 797) | 7 Statistical concept of probability | |
| 798) | 8 Subjective conception of probability | |
| 799) | 9 Axiomatic setting of probability | |
| 800) | C8) TRANSMISSION NUMBERS: | |
| 801) | 1 Rational numbers and irrational numbers | |
| 802) | 2 Algebraic numbers and transcendent numbers | |
| 803) | C9) NUMBER OF SOLUTIONS OF A POLYNOMIAL EQUATION: | |
| 804) | C10) LANGUAGE AND REASONING IN MATHEMATICS: | |
| 805) | FIFTH YEAR | |
| 806) | : 21) FUNCTIONS AND THEIR PROPERTIES: | |
| 807) | 1 Real functions of real variable | |
| 808) | 2 Domain of a function | |
| 809) | 3 Properties of the functions | |
| 810) | 4 Inverse function | |
| 811) | 5 Composite function | |
| 812) | 22) FUNCTION LIMITS: | |
| 813) | 1 Sets of real numbers | |
| 814) | 2 finite limits for x that tends to a finite value | |
| 815) | 3 infinite limits for x that tends to a finite value | |
| 816) | 4 finite limits for x that tends to an infinite value | |
| 817) | 5 infinite limits for x that tends to an infinite value | |
| 818) | 6 First theorems about limits | |
| 819) | 23) CALCULATION OF LIMITS AND CONTINUITY OF FUNCTIONS: | |
| 820) | 1 Limit operations | |
| 821) | 2 Indeterminate forms | |
| 822) | 3 Notable limits | |
| 823) | 4 Calculation of limits | |
| 824) | 5 Infinitesimals, infinities and their comparison | |
| 825) | 6 Continuous functions | |
| 826) | 7 Theorems on continuous functions | |
| 827) | 8 Points of discontinuity of a function | |
| 828) | 9 Asymptotes | |
| 829) | 10 Search for asymptotes | |
| 830) | 11 Probable graph of a function | |
| 831) | 24) SUCCESSIONS AND SERIES: | |
| 832) | 1 Numerical sequences | |
| 833) | 2 progressions | |
| 834) | 3 Some properties of the sequences | |
| 835) | 4 Limit of a succession | |
| 836) | 5 Calculation of the limit of a succession | |
| 837) | 6 Induction principle | |
| 838) | 7 What is a series | |
| 839) | 8 Converging, divergent, indeterminate series | |
| 840) | 25) DERIVATIVES: | |
| 841) | 1 Derivative of a function | |
| 842) | 2 Fundamental derivatives, | |
| 843) | 3 Operations with derivatives | |
| 844) | 4 Derivative of a composite function | |
| 845) | 5 Derivative of [f (x)] ^ g (x) | |
| 846) | 26) DIFFERENTIAL CALCULATION THEOREMS: | |
| 847) | 1 Rolle's theorem | |
| 848) | 2 Lagrange theorem | |
| 849) | 3 Consequences of the Lagrange theorem | |
| 850) | 4 Cauchy theorem | |
| 851) | 5 De l'Hospìtal theorem | |
| 852) | 27) MAXIMUM, MINIMUM AND FLEXI: | |
| 853) | 1 Definitions | |
| 854) | 2 Maximum, minimum, horizontal inflections and first derivative | |
| 855) | 3 Flexes and second derivative | |
| 856) | 4 Next maxima, minima, inflections and derivatives | |
| 857) | 5 Optimization problems | |
| 858) | 28) FUNCTION STUDY: | |
| 859) | 1 Study of a function | |
| 860) | 2 Graphs of a function and its derivative | |
| 861) | 3 Applications of the study of a function | |
| 862) | 4 Approximate resolution of an equation | |
| 863) | 29) INDEFINITE INTEGRALS: | |
| 864) | 1 Immediate indefinite integrals | |
| 865) | 2 Integration by substitution | |
| 866) | 3 Integration by parts | |
| 867) | 4 Integration of fractional rational functions | |
| 868) | 30) INTEGRALS · DEFINED: | |
| 869) | 1 Fundamental theorem of integral calculus | |
| 870) | 2 Area calculation | |
| 871) | 3 Calculation of volumes | |
| 872) | 4 Volume of a rotating solid | |
| 873) | 5 Improper integrals | |
| 874) | 6 Applications of integrals to physics | |
| 875) | 7 Numerical integration | |
| 876) | 31) DIFFERENTIAL EQUATIONS: | |
| 877) | 1 What is a differential equation | |
| 878) | 2 First order differential equations | |
| 879) | 3 Second order differential equations | |
| 880) | 4 Differential equations and physics | |
| 881) | 32) PROBABILITY DISTRIBUTIONS: | |
| 882) | 1 Discrete random variables and probability distributions | |
| 883) | 2 Characterizing values of a discrete random variable | |
| 884) | 3 Frequently used probability distributions | |
| 885) | 4 Random games | |
| 886) | 5 Standardized random variables | |
| 887) | 6 Continuous random variables | |
| 888) | C8) TRANSMISSION NUMBERS: | |
| 889) | 1 Rational numbers and irrational numbers | |
| 890) | 2 Algebraic numbers and transcendent numbers | |
| 891) | 3 Calcolo dei volumi | |
| 892) | C9) NUMBER OF SOLUTIONS OF A POLYNOMIAL EQUATION: | |
| 893) | 1 Polynomial functions and equations | |
| 894) | 2 Approximate calculation of a solution | |
| 895) | C10) LANGUAGE AND REASONING IN MATHEMATICS: | |
| 896) | 1 Demonstrations and patterns of reasoning | |
| 897) | 2 Validity of reasoning schemes | |
| 898) | C11) GEOMETRIES AND FOUNDATIONS: | |
| 899) | 1 Elements of Euclid | |
| 900) | 2 Non-Euclidean geometries | |
| 901) | 3 Fundamentals of mathematics |