Mathematics for university students. Contains polynomials, trigonometric functions, sequences and series, differentiation and more.

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- 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

- 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

- 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

- 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

- 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

- Definition
- The notions of sequence and series
- Arithmetic series
- Geometric series

- Convergence
- Convergence
- Monotonic sequences
- Divergence

- Rules
- Rules for limits of sequences

- Power series
- Power series
- Convergence criteria

- Length
- Length

- Applications
- Applications of sequences and series

- 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

- 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

- 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

- 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