Lectures related to Differential equation

Differential Equations: Speed Variation Analysis

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

Canonical Transformations: Existence and Equations

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

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

Maximum Entropy Principle: Stochastic Differential Equations

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Material Point Model: Basics

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

One Dimensional Harmonic Oscillator

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

Numerical Analysis: Stability in ODEs

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

Advanced Analysis II: Differential Equations and Timers

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

Vertical Metronome: Equilibrium and Stability

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

Maximum Principle in Heat Equation

Explores the maximum principle in the context of the heat equation and the concept of the cylinder.

Higher Order Methods: Iterative Techniques

Covers higher order methods for solving equations iteratively, including fixed point methods and Newton's method.

Cauchy-Euler Equations

Covers the definition and solution of Cauchy-Euler equations, which are second-order differential equations with specific form and solutions.

Separable Differential Equations

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

Variational Methods in Mechanics

Covers variational methods in mechanics, focusing on the Ritz-Galerkin method.

Differential Equations: Solution Methods

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

Kinetic Energy of Rotating Discs and Bars

Covers kinetic energy, motion equations, and modeling of rotating discs and bars.

Canonical Transformations: Hamilton-Jacobi Equation

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Differential Equations: Initial Conditions and Solutions

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

Applications of Trigonometric Functions

Covers various applications of trigonometric functions, such as calculating values using inverse trigonometric functions.

Hamiltonian Formalism: Harmonic Oscillator

Explores the Hamiltonian formalism for the harmonic oscillator, focusing on deriving Lagrangian and Hamiltonian, isolating the system, and generating new conserved quantities.