Lectures related to Contour integration

Integration Techniques: Change of Variable and Integration by Parts

Explores advanced integration techniques such as change of variable and integration by parts to simplify complex integrals and solve challenging integration problems.

Analytic Continuation: Residue Theorem

Covers the concept of analytic continuation and the application of the Residue Theorem to solve for functions.

Inverse Z Transform: Properties and Linear Systems

Explores the inverse Z transform, properties of linear systems, and signal decomposition.

Inverse Laplace Transform: Examples

Covers the inverse Laplace transform with examples and methods for solving complex roots.

Trigonometric Integrals: Residues Method

Covers the calculation of integrals using the residues method and discusses singularities, poles, and examples.

Numerical Integration: Composite Formulas

Explores numerical integration through composite formulas, accuracy estimation, and error evaluation in integration methods.

Complex Analysis: Cauchy Integral Formula

Explores the Cauchy integral formula in complex analysis and its applications in evaluating complex integrals.

Complex Analysis: Derivatives and Integrals

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

Inverse Limits and Topologies

Explores inverse limits, profinite completions, and Hausdorff topologies in group theory and topology.

Complex Integration and Cauchy's Theorem

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.

Residue Theorem: Applications in Complex Analysis

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

Proof of Explicit Formula

Covers the proof of the explicit formula for the non-vanishing of the zeta function at the 1-line.

Unclosed Curves Integrals

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

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.

Fourier Transform and Residue Calculus

Explores Fourier transform calculation and residue calculus in mathematical analysis.

Fourier Transform: Residue Method

Covers the calculation of Fourier transforms using the residue method and applications in various scenarios.

Mellin Transform: Residue Method

Covers the calculation of Mellin transforms using the residue method and provides examples of its application.

Applications of Residue Theorem in Complex Analysis

Covers the applications of the Residue theorem in evaluating complex integrals related to real analysis.

Integration of Path: Part 2

Covers the continuation of path integrals, focusing on complex functions and their applications.

Laurent Series and Residue Theorem: Complex Analysis Concepts

Discusses Laurent series and the residue theorem in complex analysis, providing examples and applications for evaluating complex integrals.