А.Е.Әбілқасымова, К.Д.Шойынбеков. Алгебра және анализ бастамалары (Қоғамдық-гуманитарлық бағыт), 2010
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А.Е.Әбілқасымова
К.Д.Шойынбеков.
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А.Е.Әбілқасымова, К.Д.Шойынбеков. Алгебра және анализ бастамалары (Қоғамдық-гуманитарлық бағыт), 2010
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1
Entries
48
Preface
Other
Page 5
Chapter I. Function, its properties and graph
Theory
Page 7
§ 1. Concept of a function and ways of defining it
Theory
Page 7
§ 2. Simple transformations of function graphs
Theory
Page 14
§ 3. Properties of a function
Theory
Page 18
§ 4. Studying a function and plotting its graph
Theory
Page 25
Test tasks
Test
Page 29
Historical information
Other
Page 33
What did you learn in this chapter?
Open question
Page 34
Chapter II. Trigonometric functions
Theory
Page 35
§ 5. Converting trigonometric functions given as sums and differences into products
Theory
Page 35
§ 6. Converting trigonometric functions given as products into sums or differences
Theory
Page 40
§ 7. Main properties and graphs of trigonometric functions
Theory
Page 43
§ 8. Inverse trigonometric functions
Theory
Page 49
§ 9. Simple trigonometric equations and their solution
Theory
Page 58
§ 10. Methods for solving trigonometric equations and systems of equations
Theory
Page 65
§ 11. Solving trigonometric inequalities
Theory
Page 72
Test tasks
Test
Page 77
Historical information
Other
Page 81
What did you learn in this chapter?
Open question
Page 82
Chapter III. Derivative
Theory
Page 83
§ 12. Concept of the limit of a function at a point and continuity of a function
Theory
Page 83
§ 13. Definition of the derivative
Theory
Page 87
§ 14. Rules for finding derivatives
Theory
Page 92
§ 15. Physical and geometric meaning of the derivative. Tangent to a function graph
Theory
Page 97
§ 16. Derivative of a composite function
Theory
Page 103
§ 17. Derivatives of trigonometric functions
Theory
Page 105
§ 18. Approximate calculations
Theory
Page 109
Test tasks
Test
Page 112
Historical information
Other
Page 114
What did you learn in this chapter?
Open question
Page 115
Chapter IV. Applying the derivative to studying functions
Theory
Page 116
§ 19. Criteria for increasing and decreasing functions
Theory
Page 116
§ 20. Critical points. Extrema of a function
Theory
Page 120
§ 21. Studying a function using the derivative and plotting its graph
Theory
Page 124
§ 22. Greatest and least values of a function
Theory
Page 127
Test tasks
Test
Page 132
Historical information
Other
Page 135
What did you learn in this chapter?
Open question
Page 136
Chapter V. Combinatorics and Newton's binomial theorem
Theory
Page 137
§ 23. Basic elements of combinatorics
Theory
Page 137
§ 24. Newton's binomial theorem
Theory
Page 144
Test tasks
Test
Page 148
Historical information
Other
Page 149
What did you learn in this chapter?
Open question
Page 151
Exercises for review
Problem
Page 152
Subject index
Other
Page 160
Answers
Answer
Page 162
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