Lectures related to Advanced Analysis II: Generalisations and Gradients

Taylor Series: Derivatives and Integrals

Explores Taylor series expansions for derivatives and integrals, including practical applications.

Residue Theorem: Applications in Complex Analysis

Discusses the residue theorem and its applications in calculating complex integrals.

Residue Theorem: Applications in Complex Analysis

Discusses the residue theorem and its applications in complex analysis, including integral calculations and Laurent series.

Cauchy Problem Resolution: Differential Equations Overview

Covers the resolution of a Cauchy problem for a first-order linear differential equation, detailing the construction of its general solution and the determination of initial conditions.

Understanding Normal Vectors in Calculus

Delves into normal vectors in calculus, clarifying their role in integrals and parameterization of edges.

Green's Functions in Laplace Equations

Covers the concept of Green's functions in Laplace equations and their solution construction process.

Complex Analysis: Derivatives and Integrals

Provides an overview of complex analysis, focusing on derivatives, integrals, and the Cauchy theorem.