Calculus

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

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Course content

Functions

Sets

Functions

Range

Injectivity

End of Functions

Polynomials and Rational Functions

Polynomials

Linear Polynomials

Quadratic Polynomials

Factorization of Polynomials

Rational functions

End of Polynomials and Rational Functions

Trigonometric Functions

Basics

Calculation

More trigonometric functions

End of Trigonometric Functions

Exponential and Logarithmic Functions

Definition Exp

Definition Log

Growth

End of Exponential and Logarithmic Functions

Limits

Definition

Rules for calculating limits

Exponential and trigonometric functions

End of Limits

Sequences and Series

Definition

Convergence

Rules

Power Series

Length

End of Sequences and Series

Continuity

Definition of continuity

Min-max and Intermediate Value Theorem

Limits

End of Continuity

Differentiation

Definition

Simple rules

More rules

Exp and Log

End of Differentiation

Analysis of Functions

Minima and maxima

Higher derivatives

Implicit derivatives

Approximation with Polynomials

De L'Hôpital

End of Analysis of Functions

Integration

Antiderivation

Area

Integral

Estimates

The Fundamental Theorem of Calculus

End of Integration

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