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HANDBOOK ON MATHEMATICS, SCHOOL MATHEMATICS, HIGHER MATHEMATICS

All lectures: All lectures at the Academy of Intelligence on the discipline: handbook on mathematics, school mathematics, higher mathematics. These fascinating lectures provide us with the opportunity to explore the deep principles and phenomena underlying our knowledge and our desire to understand the world.
1. Math Handbook
2. Differentiation rules
3. Derivatives of simple functions, a table of derivatives
4. Derivatives table, logarithmic and exponential functions
5. Derivatives table, trigonometric functions
6. Derivatives table, hyperbolic functions
7. Integral table, integral of a rational function
8. The integral table, the integral of the logarithmic function
9. The integral table, the integral of the exponential function. The improper integral.
10. Table of integrals, integral of irrational function
11. Greek alphabet
12. Latin alphabet
13. Mathematical constants
14. Physical constants
15. Types of algebraic equations
16. Linear equation definition, examples of solutions
17. Quadratic equation
18. Cubic equation
19. Biquadratic equation
20. Return (algebraic) equation
21. Modified and generalized equations of the fourth degree
22. Generalized return equation
23. Fourth degree equation of general type
24. Two-term algebraic equation of nth degree
25. Special case of equation
26. Return (algebraic) equation
27. Algebraic equation of the nth degree of the general form
28. Types of systems of linear algebraic equations
29. A system of two linear algebraic equations
30. A system of m linear algebraic equations
31. Ordinary differential equations of the first order
32. Autonomous equation
33. Equation with separable variables
34. Linear differential equation
35. Bernoulli equation
36. Homogeneous equation
37. Special type Riccati equation
38. Special type Riccati equation, case 1
39. A special type of Riccati equation, case 2 y '= f (x) y2 + ay - ab - b2f (x).
40. Riccati equation of a special type, case 3 y '= y2 + xf (x) y + f (x).
41. Special type Riccati equation, case 4 y '= f (x) y2 - axnf (x) y + anxn-1
42. Special Riccati equation, case 5 y '= f (x) y2 + anxn-1 - a2x2nf (x).
43. Riccati equation of special type, case 6 y '= - (n + 1) xny2 + xn + 1f (x) y - f (x).
44. A special type of Riccati equation, case 7 xy '= f (x) y2 + ny + ax2nf (x).
45. Special Riccati equation, case 8 xy '= x2nf (x) y2 + [axnf (x) - n] y + bf (x).
46. Riccati equation of a special type, case 9 y '= f (x) y2 + g (x) y - a2f (x) - ag (x).
47. Special Riccati equation, case 10 y '= f (x) y2 + g (x) y + anxn-1 λ a2x2nf (x) λ axng (x).
48. A special type of Riccati equation, case 11 y '= aeλxy2 + aeλxf (x) y + λf (x).
49. Special Riccati equation, case 12 y '= f (x) y2 - aeλxf (x) y + aλeλx.
50. Riccati equation of special type, case 13 y '= f (x) y2 + aλeλx - a2e2λxf (x).
51. Special type Riccati equation, case 14 y '= f (x) y2 + λy + ae2λxf (x)
52. Riccati equation of special type, case 15 y '= y2 - f2 (x) + f' (x).
53. Special type Riccati equation, case 16 y '= f (x) y2 - f (x) g (x) y + g' (x)
54. Riccati equation of a special type, the general form y '= f (x) y2 + g (x) y + h (x).
55. The exponential form of a complex number
56. Degrees
57. The roots
58. Polynomial Horner scheme of the division of P (x) by (x-x0) Bezout theorem
59. Functions Domain of definition and values ​​Parity and oddness Periodicity Increasing, decreasing function Conversion of graphs of functions
60. Derivative Rules for calculating derivatives Derivatives table Equation tangent
61. Newton's formula - Leibniz primitive (indefinite integral). Integral table.
62. Numeric sets
63. Names and designations of numerical intervals on the coordinate line
64. Signs of the divisibility of integers
65. The law of addition and multiplication of numbers
66. Real Number Module
67. Abbreviated Multiplication Formulas
68. Degrees (m, n are integers)
69. Square roots (a ≥ 0, b ≥ 0)
70. Degree with a rational indicator
71. Proportion
72. The quadra equation ax² + bx + c (a ≠ 0) and the Vieta theorem
73. Arithmetic and Geometric Progression
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