А.Н.Колмогоров, А.М.Абрамов. Алгебра және анализ бастамалары 10-11-сынып, 2004
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А.Н.Колмогоров
А.М.Абрамов.
10-сынып
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А.Н.Колмогоров, А.М.Абрамов. Алгебра және анализ бастамалары 10-11-сынып, 2004
Preparing book pages
1
Entries
103
Preface
Other
Page 5
Chapter I. Trigonometric functions
Theory
Page 6
§ 1. Trigonometric functions of a numerical argument
Theory
Page 6
1. Sine, cosine, tangent and cotangent (review)
Theory
Page 6
2. Trigonometric functions and their graphs
Theory
Page 10
§ 2. Main properties of functions
Theory
Page 18
3. Functions and their graphs
Theory
Page 18
4. Simple transformations of function graphs
Theory
Page 22
5. Even and odd functions. Periodic functions
Theory
Page 27
6. Periodicity of trigonometric functions
Theory
Page 32
7. Increasing and decreasing functions. Extrema
Theory
Page 36
8. Increasing and decreasing trigonometric functions
Theory
Page 42
9. Studying functions
Theory
Page 45
§ 3. Solving trigonometric equations and inequalities
Theory
Page 52
10. Arcsine, arccosine and arctangent
Theory
Page 52
11. Solving simple trigonometric equations
Theory
Page 58
12. Solving simple trigonometric inequalities
Theory
Page 65
13. Examples of solving trigonometric equations and systems of equations
Theory
Page 71
Historical information
Other
Page 75
Questions and problems for review
Problem
Page 82
Chapter II. Derivative and its applications
Theory
Page 90
§ 4. Derivative
Theory
Page 90
14. Increment of a function
Theory
Page 90
15. Concept of derivative
Theory
Page 93
16. Continuity of a function and the concept of passage to the limit
Theory
Page 101
17. Derivatives of a sum, product, quotient and power function
Theory
Page 105
18. Derivative of a composite function
Theory
Page 111
19. Derivatives of trigonometric functions
Theory
Page 114
§ 5. Applications of continuity and the derivative
Theory
Page 117
20. Application of continuity
Theory
Page 117
21. Tangent to the graph of a function
Theory
Page 122
§ 6. Applying the derivative to studying functions
Theory
Page 128
22. Criterion for increasing (decreasing) functions
Theory
Page 128
23. Critical points, maxima and minima of a function
Theory
Page 132
24. Examples of applying the derivative to studying functions
Theory
Page 137
25. Greatest and least values of a function
Theory
Page 141
Historical information
Other
Page 146
Questions and problems for review
Problem
Page 157
Chapter III. Probability theory
Theory
Page 161
§ 7. Elements of probability theory
Theory
Page 161
26. Random event
Theory
Page 161
27. Probability of an event
Theory
Page 165
28. Statistical definition of probability. Addition and multiplication rules
Theory
Page 172
29. Basic concepts of combinatorics
Theory
Page 177
30. Addition of probabilities
Theory
Page 183
31. Multiplication of probabilities
Theory
Page 188
Problems for review
Problem
Page 193
Main topics of Chapter III
Other
Page 195
Chapter IV. Antiderivative and integral
Theory
Page 198
§ 8. Antiderivative
Theory
Page 198
32. Definition of an antiderivative
Theory
Page 198
33. Main property of an antiderivative
Theory
Page 201
34. Three rules for finding antiderivatives
Theory
Page 206
§ 9. Integral
Theory
Page 210
35. Area of a curvilinear trapezoid
Theory
Page 210
36. Integral. Newton-Leibniz formula
Theory
Page 214
37. Applications of the integral
Theory
Page 219
Historical information
Other
Page 223
Questions and problems for review
Problem
Page 229
Chapter V. Exponential and logarithmic functions
Theory
Page 232
§ 10. Generalization of the concept of power
Theory
Page 232
38. nth root and its properties
Theory
Page 232
39. Irrational equations
Theory
Page 238
40. Power with a rational exponent
Theory
Page 242
§ 11. Exponential and logarithmic functions
Theory
Page 249
41. Exponential function
Theory
Page 249
42. Solving exponential equations and inequalities
Theory
Page 254
43. Logarithms and their properties
Theory
Page 258
44. Logarithmic function
Theory
Page 263
45. Solving logarithmic equations and inequalities
Theory
Page 284
§ 12. Derivatives of exponential and logarithmic functions
Theory
Page 288
46. Derivative of the exponential function
Theory
Page 288
47. Derivative of the logarithmic function
Theory
Page 293
48. Power function
Theory
Page 297
Historical information
Other
Page 301
Questions and problems for review
Problem
Page 305
Chapter VI. Real numbers
Theory
Page 293
§ 13. Real numbers
Theory
Page 309
49. Rational and irrational numbers
Theory
Page 309
50. Decimal approximations of real numbers
Theory
Page 312
51. Basic properties of real numbers
Theory
Page 315
§ 14. Equations and inequalities with absolute values
Theory
Page 316
52. Equations with absolute value signs
Theory
Page 316
53. Inequalities with absolute values
Theory
Page 319
§ 15. Equations and inequalities with a parameter
Theory
Page 321
54. Equation with a parameter
Theory
Page 321
55. Inequality with a parameter
Theory
Page 323
Questions and problems for review
Problem
Page 325
Chapter VII. Probability theory and mathematical statistics
Theory
Page 310
§ 16. Elements of probability theory
Theory
Page 326
56. Random variables
Theory
Page 326
57. Distribution law of a random variable
Theory
Page 333
58. Distribution law of the sum and product of random variables
Theory
Page 337
59. Numerical characteristics of a random variable
Theory
Page 346
60. Variance and standard deviation of a random variable
Theory
Page 352
§ 17. Elements of mathematical statistics
Theory
Page 357
61. Sample
Theory
Page 357
62. Polygon and histogram
Theory
Page 362
63. Some numerical characteristics of a sample
Theory
Page 366
64. Sample variance
Theory
Page 370
Exercises for review
Problem
Page 374
Main topics of Chapter VII
Other
Page 379
Answers and hints to exercises
Answer
Page 384
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