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Ordering of infinite sets

Limits of infinite sequences

Properties of functions

Limits and continuous functions

Transcendental and real numbers

Univariate differentiation

Identifying and evaluating \(e\)

Univariate integration

The sine and cosine functions, and identifying \(\pi\)

The tangent function, and evaluating \(\pi\)

Polar coordinates

Other trigonometric functions

Taylor and Fourier analysis

The gamma and beta functions

Ordinary Differential Equations (ODEs)

Univariate optimisation

Multivariate functions

Multivariate differentiation of scalar fields

Multivariate integration of scalar fields

Multivariate differentiation of vector fields

Multivariate integration of vector fields

Partial Differential Equations (PDEs)

Multivariate optimisation

Complex calculus

Laplace transforms

Quadratic maps, the logistic map, the Mandlebrot set and the Julia set

Riemann surfaces

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