Differential Equations: Solutions and Derivatives

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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.

Canonical Transformations: Existence and Equations

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

Semi-groups of Contractions

Explores semi-groups of contractions, discussing uniqueness theorems, maximum principles, and the infinitesimal generator.

Differential Equations: Implicit Solutions

Explores implicit solutions for differential equations and their applications in different scenarios.

Differential Equations: Mathematical Complements

Covers the definition of differential equations and their relation to functions and derivatives.

Fourier Transform: Derivatives and Formulas

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

Advanced Analysis II: Sequences and Integrals

Explores sequences, integrals, symmetrical functions, differential equations, and the Cauchy problem in advanced analysis.

First Order Differential Equation

Covers first-order differential equations, including linear equations and applications in physics.

Ordinary Differential Equations: Definitions and Examples

Covers ordinary differential equations, their orders, examples, and applications in various fields.

Differential Equations: Speed Variation Analysis

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