Differential Equations: Modeling Physical and Biological Phenomena

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Partial Derivatives and Differential Equations

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Advanced Analysis: Differential Equations Overview

Covers the fundamentals of differential equations, their properties, and methods for finding solutions through various examples.

Canonical Transformations: Hamilton-Jacobi Equation

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Differential Equations: Solutions and Periodicity

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Ordinary Differential Equations: Basics

Introduces the basics of ordinary differential equations, exploring existence, uniqueness, higher dimensions, Lipschitz functions, and solution finding.

Differential Equations Solutions

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

Numerical Analysis: Stability in ODEs

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

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.

Existence and Uniqueness of Local Solutions

Explores the proof of existence and uniqueness of local solutions for a Cauchy problem with separable variables.

Advanced Analysis II: Cauchy Problem and Differential Equations

Covers the Cauchy problem in differential equations, focusing on initial conditions and their impact on solution uniqueness.