Mordkovich A.G. Algebra i nachala analiza. 10-11 klass, uchebnik (2001)(ru)(L)(T)(168s)_MSch_
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Мордкович А.Г.
Mordkovich
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Mordkovich A.G. Algebra i nachala analiza. 10-11 klass, uchebnik (2001)(ru)(L)(T)(168s)_MSch_
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Entries
76
Preface for the teacher
Other
Page 3
Chapter 1. Trigonometric functions
Theory
Page 5
§ 1. Introduction
Theory
Page 5
§ 2. Number circle
Theory
Page 8
§ 3. Number circle on the coordinate plane
Theory
Page 17
§ 4. Sine and cosine
Theory
Page 25
§ 5. Tangent and cotangent
Theory
Page 32
§ 6. Trigonometric functions of a numerical argument
Theory
Page 35
§ 7. Trigonometric functions of an angular argument
Theory
Page 37
§ 8. Reduction formulas
Theory
Page 41
§ 9. The function y = sin x, its properties and graph
Theory
Page 43
§ 10. The function y = cos x, its properties and graph
Theory
Page 49
§ 11. Periodicity of the functions y = sin x and y = cos x
Theory
Page 51
§ 12. How to construct the graph of y = mf(x) if the graph of y = f(x) is known
Theory
Page 53
§ 13. How to construct the graph of y = f(kx) if the graph of y = f(x) is known
Theory
Page 56
§ 14. Graph of harmonic oscillation
Theory
Page 60
§ 15. The functions y = tan x and y = cot x, their properties and graphs
Theory
Page 61
Main results
Theory
Page 67
Chapter 2. Trigonometric equations
Theory
Page 69
§ 16. First ideas about solving trigonometric equations
Theory
Page 69
§ 17. Arccosine. Solving the equation cos t = a
Theory
Page 72
§ 18. Arcsine. Solving the equation sin t = a
Theory
Page 77
§ 19. Arctangent and arccotangent. Solving the equations tan x = a, cot x = a
Theory
Page 83
§ 20. Trigonometric equations
Theory
Page 89
Main results
Theory
Page 100
Chapter 3. Transformation of trigonometric expressions
Theory
Page 101
§ 21. Sine and cosine of a sum of arguments
Theory
Page 101
§ 22. Sine and cosine of a difference of arguments
Theory
Page 105
§ 23. Tangent of a sum and difference of arguments
Theory
Page 108
§ 24. Double-angle formulas
Theory
Page 110
§ 25. Power-reduction formulas
Theory
Page 115
§ 26. Transforming sums of trigonometric functions into products
Theory
Page 117
§ 27. Transforming products of trigonometric functions into sums
Theory
Page 122
§ 28. Transforming A sin x + B cos x into the form C sin(x + t)
Theory
Page 123
Main results
Theory
Page 126
Chapter 4. Derivative
Theory
Page 128
§ 29. Numerical sequences
Theory
Page 128
§ 30. Limit of a numerical sequence
Theory
Page 131
§ 31. Limit of a function
Theory
Page 140
§ 32. Definition of the derivative
Theory
Page 148
§ 33. Calculation of derivatives
Theory
Page 155
§ 34. Equation of the tangent to the graph of a function
Theory
Page 165
§ 35. Using the derivative to study monotonicity and extrema of functions
Theory
Page 170
§ 36. Using the derivative to find greatest and least values of quantities
Theory
Page 184
Main results
Theory
Page 192
Chapter 5. Antiderivative and integral
Theory
Page 194
§ 37. Antiderivative and indefinite integral
Theory
Page 194
§ 38. Definite integral
Theory
Page 202
Main results
Theory
Page 212
Chapter 6. Powers and roots. Power functions
Theory
Page 213
§ 39. Concept of the nth root of a real number
Theory
Page 213
§ 40. Function of the form y = ⁿ√x, its properties and graph
Theory
Page 217
§ 41. Properties of the nth root
Theory
Page 223
§ 42. Transformation of expressions containing radicals
Theory
Page 228
§ 43. Generalization of the concept of exponent
Theory
Page 231
§ 44. Power functions, their properties and graphs
Theory
Page 235
Main results
Theory
Page 243
Chapter 7. Exponential and logarithmic functions
Theory
Page 245
§ 45. Exponential function, its properties and graph
Theory
Page 245
§ 46. Exponential equations
Theory
Page 256
§ 47. Exponential inequalities
Theory
Page 259
§ 48. Concept of logarithm
Theory
Page 261
§ 49. The function y = log_a x, its properties and graph
Theory
Page 264
§ 50. Properties of logarithms
Theory
Page 270
§ 51. Logarithmic equations
Theory
Page 276
§ 52. Logarithmic inequalities
Theory
Page 279
§ 53. Change of base of a logarithm
Theory
Page 282
§ 54. Differentiation of exponential and logarithmic functions
Theory
Page 285
Main results
Theory
Page 293
Chapter 8. Equations and inequalities. Systems of equations and inequalities
Theory
Page 294
§ 55. Equivalence of equations
Theory
Page 294
§ 56. General methods for solving equations
Theory
Page 302
§ 57. Solving inequalities in one variable
Theory
Page 308
§ 58. Systems of equations
Theory
Page 318
§ 59. Equations and inequalities with parameters
Theory
Page 327
Main results
Theory
Page 338
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