Brunei Math Club

Euclidean Spaces

Open Sets and Closed Sets in R^n

Multivariate functions: Limits and Continuity

Maps from R^n to R^m

Partial and Total Differentiation of Multivariate Functions

Total differentiability implies continuity

Multivariate Chain Rules

Higher-order partial differentiation

Differential operators

Multivariate Taylor expansion

Extreme values of multivariate functions

Implicit functions

Uniform convergence of sequence of functions

A continuous function may not be differentiable

Marginal distributions of the multivariate Normal distribution are normal.

Limit Superior and Limit Inferior

Mathematical Methods II: Differentiation of Multivariate Functions (1) Part 2

Computing integrals [Mathematical Methods I (12-3)]

Collections of periodic functions

What is a differentiable function?

Simple proof that any covariance matrix is positive semi-definite

Fourier Series of Piece-wise Smooth Functions

Properties of integrals [Mathematical Methods I (12-2)]