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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 \(e\)

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

Polar coordinates

Power series, Taylor series and Maclaurin series

Matrix exponents and Taylor series of matrices

Univariate integration

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

Other trigonometric functions

Fourier analysis

Generalising factorials: The gamma function

First-order Ordinary Differential Equations (ODEs)

Second-order Ordinary Differential Equations (ODEs)

Univariate optimisation

Multivariate functions

Multivariate differentiation of scalar fields

Multivariate integration of scalar fields

Generalising the binomial coefficient formula: The beta function

Multivariate differentiation of vector fields

Multivariate integration of vector fields

Partial Differential Equations (PDEs)

Multivariate optimisation of scalar fields

Variational calculus/functionals

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