Lectures related to Differential Equations: Introduction and Theoretical Results

Differential Equations: Initial Conditions and Solutions

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

One Dimensional Harmonic Oscillator

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

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Partial Derivatives and Differential Equations

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Material Point Model: Basics

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

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.

Separable Differential Equations

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

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.

Differential Equations: Solutions and Derivatives

Explores differential equations solutions, derivatives, differentiability, composite functions, and continuous functions.

Differential Equations: Solutions and Uniqueness

Explores differentiability, continuity, solutions, and uniqueness in differential equations, emphasizing well-posed problems and real-world applications.

Differential Equations Solutions

Covers solutions of differential equations with initial conditions and boundedness concepts.

Homogeneous Differential Equations

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

Differential Equations: Solutions and Functions

Explores solutions of differential equations and properties of functions.

Differential Equations: Solution Methods

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

Vertical Metronome: Equilibrium and Stability

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

Path Integral Representation of Propagators

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

Addition of Springs: General Physical Exercises I

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

Linear Differential Equations

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