Lectures related to Separation of Variables

Quantum Mechanics: Power Series Solutions

Explores power series solutions in quantum mechanics for differential equations and energy quantization.

Numerical Analysis: Stability in ODEs

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

Sturm-Liouville Problem: Legendre Equation

Explores the Sturm-Liouville problem linked to the Legendre equation and its significance in physics.

Quantum Field Theory: Fermions and Grassmann Numbers

Explores quantum field theory, focusing on fermions and Grassmann numbers in the path integral formalism.

Differential Equations: Speed Variation Analysis

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

Differential Equations: General Solutions and Methods

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

Numerical Methods: Runge-Kutta Approximation

Covers the Runge-Kutta method for approximating solutions of differential equations.

Solving Differential Equations

Covers the process of solving differential equations using various methods.

Ordinary Differential Equations: Non-linear Analysis

Covers non-linear ordinary differential equations, including separation, Cauchy problems, and stability conditions.

Boundary Problems in 1D: Finite Differences

Covers chapter 10 on boundary problems in 1D using finite difference methods.

Gaussian Path Integrals: Composition Property

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

Rolling and Review

Covers pure rotation, rolling without slipping, and converting reference frames in physics.

Differential Equations: Solution Methods

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

Quantum Chemistry: Fundamentals of Quantum Mechanics

Covers the fundamentals of quantum mechanics and the behavior of particles at the quantum level.

Quantum Mechanics: Jacobi Identity and Gauge Invariance

Explores Jacobi identity, gauge invariance, and conservation laws in quantum mechanics and classical physics.

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.

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.

Path Integral and Gaussian Integrals

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

Introduction to ODEs: System of 1st Order ODEs

Introduces Ordinary Differential Equations (ODEs) and their applications in physics, covering basics, initial value problems, and linear ODEs.