Calculus
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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