Lectures related to Analytic Continuation: Residue Theorem

Laplace Transform: Analytic Continuation

Covers the Laplace transform, its properties, and the concept of analytic continuation.

Plasma Instabilities: Case Studies

Analyzes plasma instabilities through case studies, exploring the implications of roots in the complex plane.

Residue Theorem: Calculating Integrals on Closed Curves

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

Kinetic Theory: Distribution Function Evolution

Explores the evolution of the distribution function describing particles in phase space.

Kinetic Theory of Plasma: Linearized Vlasov Equations

Explores the kinetic theory of plasma, focusing on linearized Vlasov equations in hot magnetized plasmas and the behavior of plasma particles in phase space.

Plasma Energy Loss: Impact Parameter and Debye Screening

Covers energy loss in plasma due to impact parameter intervals and Debye screening effects.

Electrostatic Waves: Magnetic Field Interaction

Explores the interaction of electrostatic waves with the magnetic field in plasma physics.

Plasma Physics: Impact Ionisation and Random Walk

Explores impact ionisation in plasma physics and the random walk model as a key challenge in understanding plasma confinement.

Plasma Waves: Two-Fluid Model

Explores plasma waves described by the two-fluid model and the behavior of Langmuir waves.

Residue Theorem: Cauchy's Integral Formula and Applications

Covers the residue theorem, Cauchy's integral formula, and their applications in complex analysis.

Plasma Collisions: Coulomb Force

Analyzes Coulomb collisions between charged particles and the conservation of energy, momentum, and angular momentum.

Plasma Waves: Propagation and Modes

Explores the propagation and modes of plasma waves, including R- and L-waves, Langmuir waves, and Faraday rotation.

MHD Plasma Approximation

Covers the MHD plasma approximation, discussing macroscopic phenomena and phase velocities.

Applications of Residue Theorem in Complex Analysis

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

Random Walk Simulation: Mean Displacement and Diffusion Coefficient

Covers random walk simulation, mean displacement, and diffusion coefficient calculations for weakly ionized particles.

Vlasov-Maxwell System: Plasma Waves Analysis

Explores the Vlasov-Maxwell system for analyzing plasma waves in an unmagnetized plasma.

Complex Integration: Fourier Transform Techniques

Discusses complex integration techniques for calculating Fourier transforms and introduces the Laplace transform's applications.

Landau Damping in Plasma Physics

Covers the concept of Landau damping in plasma physics, focusing on the interaction between waves and particles.

Residue Theorem: Applications in Complex Analysis

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

Plasma Physics II: Non-linear Plasma Dynamics

Explores non-linear phenomena in plasma physics, focusing on ion acoustic waves and the Korteweg de Vries equation.