Lectures related to Methods of Demonstrations: Examples and Solutions

Differential Equations: Speed Variation Analysis

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

Differential Equations: Coefficients and Methods

Discusses methods for solving differential equations, focusing on undetermined coefficients and variation of constants.

Probability and Statistics

Covers mathematical concepts from number theory to probability and statistics.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Differential Equations: General Solutions and Methods

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

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.

One Dimensional Harmonic Oscillator

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

Differential Equations in Motion

Explores differential equations for motion, including critical damping and damped oscillators, with applications in complex numbers and examples of mass-spring systems.

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Path Integral and Gaussian Integrals

Covers the path integral representation of the propagator and Gaussian integrals in complex and multi-dimensional cases.

Separable Differential Equations

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

Differential Equations Solutions

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

Complex Analysis: Functions and Their Properties

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

Numerical Analysis: Stability in ODEs

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

Vertical Metronome: Equilibrium and Stability

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

Fourier Transform: Derivatives and Formulas

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

Taylor Polynomials: Correction Exam 2018

Covers the correction of an exam from 2018, focusing on Taylor polynomials and Jacobian matrices.

Linear Differential Equations

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

Inverse Laplace Transform and Cauchy Problem

Introduces the inverse Laplace transform and the Cauchy problem for ordinary differential equations, emphasizing the importance of verifying the obtained results.