Lectures related to Differential Equations and System Composition

Laplace Transform Application: LTI Systems

Covers the application of Laplace transform to LTI Systems, including examples and differential equations.

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

Explores the Fourier transform application to LTI systems, including frequency response, convolution, differentiation, and solving differential equations.

Partial Fraction Expansion

Introduces Partial Fraction Expansion as a valuable tool for analyzing stable LTI systems.

Differential Equations: Speed Variation Analysis

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

Laplace Transform: Properties and Examples

Covers the Laplace Transform, including its properties and examples.

Inverse Laplace Transform

Covers the Inverse Laplace Transform and its applications in finding projections from the Laplace domain to the time domain.

Differential and Difference Equations

Explores differential and difference equations for causal LTI systems using examples of RC circuits and vehicle motion.

One Dimensional Harmonic Oscillator

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

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.

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.

Vertical Metronome: Equilibrium and Stability

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

Convolution and Laplace Transform

Explores control of dynamic systems, impulse response, Laplace transform, and Fourier transform for solving differential equations.

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.

Electric Motors: Principles and Applications

Explores electric motor principles, linearity, control systems, active suspensions, and Laplace transforms.

Notion of Transfer Function

Introduces the concept of transfer function in dynamic systems analysis.