Methods of Demonstrations: Examples and Solutions

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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.