m21 FUNCTIONS, SUCCESSION AND THEIR PROPERTIES
Real functions of real variable
Domain of a function
Properties of functions
Reverse function
Composite function
Functions and their properties
Successions and progressions
Induction principle
m22 LIMITS
Sets of real numbers
lim f(x) = l
Limits + ∞ or -∞ as x tends to a finite value
Finite limit as x tends to +∞ or -∞
Limits + ∞ or -∞ as x tends to +∞ or -∞
The limits and their verification
first limit theorems
limit of a sequence
m23 CALCULATION OF LIMITS AND CONTINUITY
Limit operations
Indeterminate forms of limits
Notable limitations
Calculation of limits
Infinitesimals, infinities and their comparison
Calculation of the limit of a sequence
Continuous functions and limits
Theorems on continuous functions
Points of discontinuity and singularity
Asymptotes
Summary: Finding asymptotes
Probable graph of a function
m24 DERIVATE
Derivative of a function
Fundamental derivatives
Operations with derivatives
Derivative of a compound function
Operations with derivatives and compound functions
Derivative of the inverse function
Calculation of derivatives
Derivatives of higher order than the first
Tangent line
Derivative and rate of change
Differential of a function
m25 DERIVABILITY AND THEOREMS OF DIFFERENTIAL CALCULUS
Points of non-derivability
Rolle's theorem
Lagrange theorem
Consequences of Lagrange's theorem
Cauchy theorem
Theorems of Rolle, Lagrange, Cauchy
De L'Hospital's Theorem
m26 MAXIMUM, MINIMUM AND FLEXIBLE
Maxima, minima, horizontal inflections and first derivative
Relative maxima and minima and horizontal inflections
Inflexions and second derivative
Maxima, minima, inflections and successive derivatives
Optimization problems
Maxima, minima, horizontal inflections and first derivative
Relative maxima and minima and horizontal inflections
Inflexions and second derivative
Maxima, minima, inflections and successive derivatives
Optimization problems
CHAPTER 27
m27 STUDY OF FUNCTIONS
Study of a function
Graphs of a function and its derivative
Approximate resolution of an equation
m28 INDEFINITE INTEGRALS
Indefinite integral
Immediate indefinite integrals
Integration by substitution
Integration by parts
Integration of fractional rational functions
m29 DEFINED INTEGRALS
Definite integral
Fundamental theorem of integral calculus
Calculation of areas
Calculation of volumes
Volume of a solid of rotation
Improper integrals
Applications of integrals to physics
Numerical integration
m30 DIFFERENTIAL EQUATIONS
What is a differential equation
Solving some types of differential equations
First order differential equations
m30A PROBABILITY DISTRIBUTIONS
Discrete random variables and probability distributions
Values characterizing a discrete random variable
Frequently used probability distributions
Random games
Standardized random variables
Continuous random variables
C11 GEOMETRIES AND FUNDAMENTALS
Euclid's elements
Non-Euclidean geometries
Foundations of mathematics
C12 SERIES
What is a series
Convergent, divergent, indeterminate series