Lectures related to Gaussian Path Integrals: Properties and Composition

Path Integral and Gaussian Integrals

Covers the path integral representation of the propagator and Gaussian integrals in complex and multi-dimensional cases.

Path Integral Representation of Propagators

Covers the path integral representation of propagators for free particles and harmonic oscillators.

Gaussian Path Integrals: Composition Property

Explores wave packet evolution, path integrals, and Gaussian composition properties in quantum mechanics.

Gelfand-Yaglom Formula

Explores the Gelfand-Yaglom formula and time-ordered products in the context of the path integral representation of the propagator for a time-dependent harmonic oscillator.

Differential Equations: Speed Variation Analysis

Covers the analysis of speed variation using differential equations and small time intervals.

One Dimensional Harmonic Oscillator

Explores the one-dimensional harmonic oscillator, equilibrium positions, and forced oscillators with external forces.

Position Space Approach: Analyzing Banana Feynman Diagrams

Presents the position space approach to banana Feynman diagrams and their differential equations.

Canonical Transformations: Existence and Equations

Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.

Homogeneous Differential Equations

Explores solving first-order homogeneous differential equations through variable changes and delves into the Bernoulli differential equation.

Advanced Analysis II: Differential Equations and Timers

Discusses advanced analysis concepts, focusing on differential equations and timers in microcontrollers.

Material Point Model: Basics

Covers the material point model, initial conditions, and Newton's laws in physics.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Separable Differential Equations

Covers separable differential equations of order 1, defining separable equations and providing examples.

Vertical Metronome: Equilibrium and Stability

Explores equilibrium and stability of a vertical metronome system with springs.

Addition of Springs: General Physical Exercises I

Covers the addition of springs in series and parallel, exploring equivalent movements.

Differential Equations: Solution Methods

Explores the resolution of differential equations and the properties of exponential functions in electrical engineering.

Generalized Integrals: Definition and Applications

Covers the definition and applications of generalized integrals in advanced analysis, including real functions, differential equations, and multiple integrals.

Differential Equations: Initial Conditions and Solutions

Covers the solution of differential equations with initial conditions and limit analysis.

Linear Differential Equations

Explores linear differential equations, including higher-order linear homogeneous equations and equations with constant coefficients.

Numerical Integration Methods

Explores numerical integration methods and their application in solving differential equations and simulating physical systems.