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 |