Lectures related to Laplace Transform: Properties and Examples

Laplace Transform Application: LTI Systems

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

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 and System Composition

Covers Laplace transform for LTI systems and system composition.

Inverse Laplace Transform

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

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.

Advanced Analysis II: Differential Equations and Timers

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

Convolution and Laplace Transform

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

Homogeneous Differential Equations

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

Electric Motors: Principles and Applications

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

Material Point Model: Basics

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

Laplace Transform: Solving Differential Equations

Discusses the application of the Laplace transform to solve differential equations and explores its properties and examples.

Canonical Transformations: Existence and Equations

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

Numerical Analysis: Stability in ODEs

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

Laplace Transform and LTI Systems

Covers Laplace Transform, Fourier Transforms, transfer functions, LTI systems, and Region of Convergence properties.

Separable Differential Equations

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

Laplace Transforms: Applications and Convergence Properties

Introduces Laplace transforms, their properties, and applications in solving differential equations.

Differential and Difference Equations

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

Fourier Transform: Derivatives and Formulas

Explores Fourier transform properties with derivatives, crucial for solving equations, and introduces the Laplace transform for signal transformation.