1176_2- Алгебра и нач. мат. ан. 11кл (проф. ур.)_Колягин Ю.М. и др_2010 -264с
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Колягин Ю.М.
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1176_2- Алгебра и нач. мат. ан. 11кл (проф. ур.)_Колягин Ю.М. и др_2010 -264с
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Entries
69
Chapter I. Derivative and its applications
Theory
Page 4
Limit of a function. Continuous functions
Theory
Page 4
Derivative
Theory
Page 12
Rules of differentiation
Theory
Page 15
Derivative of a power function
Theory
Page 20
Derivatives of some elementary functions
Theory
Page 24
Geometric meaning of the derivative
Theory
Page 29
Increasing and decreasing functions
Theory
Page 37
Extrema of a function
Theory
Page 41
Applying derivatives to graphing functions
Theory
Page 46
Maximum and minimum values of a function
Theory
Page 51
Second derivative, convexity, and inflection points
Theory
Page 58
Exercises for Chapter I
Problem
Page 65
Historical note
Other
Page 71
Chapter II. Integral
Theory
Page 74
Antiderivative
Theory
Page 74
Rules for finding antiderivatives
Theory
Page 77
Area of a curvilinear trapezoid. Integral and its calculation
Theory
Page 81
Calculating areas using integrals
Theory
Page 89
Applying integrals to solving physics problems
Theory
Page 93
Basic differential equations
Theory
Page 95
Exercises for Chapter II
Problem
Page 98
Historical note
Other
Page 100
Chapter III. Complex numbers
Theory
Page 102
Definition of complex numbers
Theory
Page 102
Addition and multiplication of complex numbers
Theory
Page 104
Modulus of a complex number
Theory
Page 107
Subtraction and division of complex numbers
Theory
Page 108
Geometric interpretation of a complex number
Theory
Page 111
Trigonometric form of a complex number
Theory
Page 115
Properties of the modulus and argument of a complex number
Theory
Page 118
Quadratic equation with a complex unknown
Theory
Page 120
Examples of solving algebraic equations
Theory
Page 123
Exercises for Chapter III
Problem
Page 125
Historical note
Other
Page 128
Chapter IV. Elements of combinatorics
Theory
Page 130
Combinatorial problems. Multiplication rule
Theory
Page 130
Permutations
Theory
Page 132
Arrangements
Theory
Page 133
Combinations and their properties
Theory
Page 136
Newton's binomial formula
Theory
Page 139
Exercises for Chapter IV
Problem
Page 141
Historical note
Other
Page 143
Chapter V. Introduction to probability
Theory
Page 145
Probability of an event
Theory
Page 145
Addition of probabilities
Theory
Page 147
Probability of the complementary event
Theory
Page 149
Conditional probability
Theory
Page 151
Independent events
Theory
Page 155
Exercises for Chapter V
Problem
Page 157
Historical note
Other
Page 158
Chapter VI. Divisibility of integers. Integer solutions of equations
Theory
Page 160
Concept of divisibility. Divisibility of sums and products
Theory
Page 160
Division with remainder. Divisibility tests
Theory
Page 162
Congruences
Theory
Page 166
Solving equations in integers
Theory
Page 169
Exercises for Chapter VI
Problem
Page 173
Historical note
Other
Page 174
Chapter VII. Polynomials and algebraic equations
Theory
Page 175
Polynomials and arithmetic operations on them
Theory
Page 175
Division of polynomials. Horner's scheme
Theory
Page 178
Algebraic equation and its roots. Bezout's theorem
Theory
Page 183
Factorization of polynomials
Theory
Page 185
Polynomials in two and three variables
Theory
Page 188
Exercises for Chapter VII
Problem
Page 193
Historical note
Other
Page 195
Exercises for final review of the algebra course
Problem
Page 197
Problems for extracurricular work
Problem
Page 232
Answers and hints
Answer
Page 246
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