Chapter 1: Functions

- Sets
- - The notion of sets
- - Operations for sets
- - Intervals
- Functions
- - The notion of function
- - Operations for functions
- Range
- - The range of a function
- - Functions and graphs
- - Transformations of the axes
- - Symmetry of functions
- Injectivity
- - Injective functions
- - The inverse of a function
- - Power functions
- - Equations and functions
- Applications
- - Applications of functions

Chapter 2: Polynomials and rational functions

- Polynomials
- - The notion of polynomial
- - Calculating with polynomials
- - Division with remainder for polynomials
- Linear polynomials
- - Linear functions
- Quadratic polynomials
- - Quadratic functions
- - Quadratic equations
- - Quadratic inequalities
- Factorization of polynomials
- - The notions gcd and lcm for polynomials
- - Rules of calculation for gcd and lcm of polynomials
- - The Euclidean algorithm for polynomials
- - Factorization of polynomials
- - The Fundameltal Theorem of Algebra
- - Polynomial interpolation
- - The extended Euclidean algorithm for polynomials
- Rational functions
- - The notion of rational function
- - Normal form for rational functions
- - Partial fraction decomposition for rational functions
- Applications
- - Applications of polynomials and rational functions

Chapter 3: Trigonometric functions

- Basics
- - Definitions of sin and cos
- - Right triangles and trigonometric functions
- - Periodicity of trigonometric functions
- Calculation
- - Special values of trigonometric functions
- - Addition formulas for trigonometric functions
- - Triangles and trigonometric functions
- More trigonometric functions
- - Tangent and cotangent
- - Inverse trigonometric functions
- Applications
- - Applications of trigonometric functions

Chapter 4: Exponential and logarithmic functions

- Definition exp
- - The notion of exponential function
- - Rules of calculation for exponential functions
- - Equations with exponential functions
- Definition log
- - The notion of logarithm
- - Rules of calculation for logarithms
- - Equations with logarithms
- Growth
- - Exponential growth
- Applications
- - Applications of exponential and logarithmic functions

Chapter 5: Limits

- Definition
- - The notion of limit
- - The notion of limit and infinity
- - Limits of rational functions
- - Vertical asymptotes
- Rules for calculating limits
- - Rules for limits
- - Horizontal asymptotes
- - Oblique asymptotes
- - Squeeze theorem for limits
- Exp and gonio
- - Limits of exponential functions
- - Trigonometric limits
- Applications
- - Applications of limits

Chapter 6: Sequences and series

- Definition
- - The notions of sequence and series
- - Arithmetic series
- - Geometric series
- Convergence
- - Convergence
- - Monotonic sequences
- - Divergence
- Rules
- - Rules for limits and sequences
- Power series
- - Power series
- - Convergence criteria
- Length
- - Length
- Applications
- - Applications of sequences and series

Chapter 7: Continuity

- Definition of continuity
- - The notion of continuity
- - Global minimum and maximum
- - Continuous extension
- Min-max and Intermediate Value Theorem
- - The Min-Max Theorem
- - Intermediate Value Theorem
- Limits
- - Limits of continuous functions
- - Rules for continuity
- Applications
- - Applications of continuity

Chapter 8: Differentiation

- Definition
- - The notion of difference quotient
- - The notion of differentiation
- - A simple derivative
- Simple rules
- - The derivative of a sum function
- - The derivative of a polynomial
- - The product rule for differentiation
- - Tangent lines
- More rules
- - The chain rule for differentiation
- - Derivatives of trigonometric functions
- - The quotient rule for differentiation
- - Derivatives of inverse functions
- Exp and log
- - The natural logarithm
- - Derivatives of exponential and logarithmic functions
- Applications
- - Applications of differentiation

Chapter 9: Analysis of functions

- Minima and maxima
- - Local minima and maxima
- - The Mean Value Theorem
- - Monotonocity
- Higher derivatives
- - Higher derivatives
- Implicit derivatives
- - Implicit derivatives
- Approximation with polynomials
- - Linear approximation
- - Taylor series
- - Taylor series of some known functions
- De L'Hôpital
- - The De L'Hôpital rule
- Applications
- - Applications of analysis of functions

Chapter 10: Integration

- Antiderivation
- - The notion of an antiderivative
- - Antiderivatives of some known functions
- - Integration by parts
- Area
- - Area
- Integral
- - Riemann sums
- - The integral of a function
- - Rules of calculation for integrals
- Estimates
- - Estimates of integrals
- - Mean Value Theorem for integrals
- The Fundamental Theorem of Calculus
- - The Fundamental Theorem of Calculus
- Applications
- - Applications of integration