Lectures related to Probability and Statistics

Laplace Transform: Properties and Applications

Covers the properties and applications of the Laplace transform in solving differential equations.

Covers Fourier series, periodic functions, and Fourier transforms.

Transformations and Inversions: Laplace and Fourier

Discusses Laplace and Fourier transformations, focusing on their inversion formulas and applications in solving differential equations.

Advanced Analysis II: Differential Equations and Timers

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

Laplace Transforms: Applications and Convergence Properties

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

Mathematical Methods: Collision Dynamics and Energy Transfer

Covers mathematical methods for analyzing collision dynamics and energy transfer in physics.

Complex Analysis: Functions and Their Properties

Covers the fundamentals of complex analysis, focusing on complex functions, their properties, and applications in solving differential equations.

Fourier Transform: Derivatives and Formulas

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

Complex Integration: Fourier Transform Techniques

Discusses complex integration techniques for calculating Fourier transforms and introduces the Laplace transform's applications.

Fourier Transform and Differential Equations

Discusses the Fourier transform and its application to solving differential equations, focusing on the wave equation and its transformations.

Fourier and Laplace Transforms: Concepts and Applications

Provides an overview of Fourier and Laplace transforms, their properties, and applications in signal analysis.

Poisson Problem: Fourier Transform Approach

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

Fourier Transform: Concepts and Applications

Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.

Differential Equations: Solutions and Monotonicity

Explores solutions of differential equations and their monotonicity properties.

Differential Equations: Implicit Function Theorem Applications

Discusses the reduction of higher-order differential equations to first-order systems using the implicit function theorem.

Applications of Residue Theorem in Complex Analysis

Covers the applications of the Residue theorem in evaluating complex integrals related to real analysis.

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Differential Equations: Speed Variation Analysis

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

Solutions of Differential Equations

Explores finding solutions of differential equations, emphasizing maximal solutions and general solutions with constants.

Differential Equations: Initial Conditions and Solutions

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