Advanced Calculus in Statistics

Course content

Review of Multidimensional Calculus. Derivatives of multivariable functions, continuity of multivariable functions. Fundamental Lemma for differentiability. Chain rule and Taylor`s Theorem for multivariable functions. Jacobian. Inverse and Implicit Function Theorems. Topology of R2 and R3. Riemann-Stieltjes Integral, integrability. Integrability of continuous functions, sequences of integrable functions. Bounded convergence and Riesz Representation Theorems. Theorems of Integral Calculus: Integration in Cartesian spaces. Improper and infinite integrals. Series of functions.