Calculus (NEW)

First and second-year calculus course for university and college STEM majors. Contains topics ranging from limits, sequences & series to differentiation and integration.

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Course content

Logic

Propositional logic

Calculating with propositions

Predicate logic

Logical argumentation

End of Logic

Sets

Sets

Operations on sets

Relations

Real numbers

End of Sets

Functions

Introduction

Functions

Operations for functions

Range

Injectivity

Applications

End of Functions

Polynomials and Rational Functions

Introduction to Polynomials and Rational Functions

Quadratic polynomials

Polynomials

Greatest common divisor

Factorisation of polynomials

Rational functions

End of Polynomials and Rational Functions

Trigonometric Functions

Introduction to Trigonometric functions

The functions sine and cosine

Calculating with sine and cosine

More trigonometric functions

End of Trigonometric Functions

Exponential and Logarithmic Functions

Introduction to Exponential and Logarithmic functions

Definition Exp

Definition Log

Growth

End of Exponential and Logarithmic Functions

Limits

Introduction to Limits

Definition of limit

Calculating with limits

Asymptotes

Limits of some non-rational functions

End of Limits

Sequences and Series

Introduction to Sequences and Series

Definition of sequence and series

Limits of sequences

Convergence of series

Power series

Completeness of the real numbers

End of Sequences and Series

Continuity

Introduction to Continuity

Definition of continuity

Three theorems on continuous functions

Limits and continuity

Continuity in geometry

End of Continuity

Differentiation

Introduction to Differentiation

Definition of differentiation

Calculating derivatives and tangent lines

Derivatives of special functions

End of Differentiation

Analysis of Functions

Introduction

Minima and maxima

Higher derivatives

Implicit derivatives

Approximation with polynomials

End of Analysis of Functions

Integration

Introduction to Integration

Antiderivatives

Definite integrals

Properties of definite integrals

Calculating with definite integrals

Finding antiderivatives

Antiderivatives of rational functions

End of Integration

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