Course

MATH-207(d): Analysis IV

Lectures in this course (26)

Summarizes the usage of complex analysis theorems for different scenarios and emphasizes precise evaluation and decision-making.

Convergence and Poles: Analyzing Complex Functions

Covers the analysis of complex functions, focusing on convergence and poles.

Complex Analysis: Holomorphic Functions

Explores holomorphic functions in complex analysis and the Cauchy-Riemann equations.

Cauchy Equations and Integral Decomposition

Covers the application of Cauchy equations and integral decomposition, addressing questions related to holomorphic functions and Jacobian matrices.

Cauchy-Riemann Equations

Explores the Cauchy-Riemann equations, holomorphic functions, and the integral formula of Cauchy.

Cauchy Theorem and Laurent Series

Covers the Cauchy theorem, the conditions to apply it, and the Laurent series.

Laurent Series: Analysis and Applications

Explores Laurent series, regularity, singularities, and residues in complex analysis.

Unclosed Curves Integrals

Covers the calculation of integrals over unclosed curves, focusing on essential singularities and residue calculation.

Residues and Singularities

Covers the calculation of residues, types of singularities, and applications of the residue theorem in complex analysis.

Laurent Series: Singularities and Convergence

Explores Laurent series, singularities, convergence, residues, and analytic functions with practical examples and calculations.

Analyzing Poles and Residues

Covers the analysis of poles and residues in complex functions, focusing on the calculation of singularities, poles, and residues.

Essential Singularity and Residue Calculation

Explores essential singularities and residue calculation in complex analysis, emphasizing the significance of specific coefficients and the validity of integrals.

Transforms Properties

Covers the properties of transforms and their applications in mathematics.

Transforms of the Place

Explores the intuition behind transforms of the place and addresses audience questions on integral calculations and function choices.

Laplace transform: properties and applications

Covers the Laplace transform properties and applications, including linearity, shift, and derivative.

Fourier Analysis: Inversion Formula

Explores the Fourier inversion formula and the importance of the integral on the half-circle being zero for the method to work.

Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Analyse IV: Laurent Series and Singularities

Covers Laurent series, singularities, and meromorphic functions, addressing convergence, holomorphicity, and residue theorem applications.

Transforming Solutions: Laplace Transform

Explores transforming solutions using the Laplace transform to solve differential equations efficiently.

Analyse IV: Rediffusion RaQ semaine 10

Explores advanced mathematical analysis topics, including Laplace transform methods and integral equations.