Lectures related to Differential Equations: Mathematical Complements

Linear Approximation and Derivative Parametric

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Partial Derivatives and Differential Equations

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

Canonical Transformations: Hamilton-Jacobi Equation

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

Optimization Problems: Algebra and Trinomial Equations

Explores optimization problems in algebra and trinomial equations, focusing on maximizing area with fixed perimeters.

Differential Equations: Solutions and Functions

Explores solutions of differential equations and properties of functions.

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.

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: Differential Equations and Timers

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

Implicit Functions Theorem

Explores the implicit functions theorem and the equation of the tangent plane in a graph.

Solutions of Differential Equations

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

Differential Equations Solutions

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

Ordinary Differential Equations: Definitions and Examples

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

Laplacian in Polar and Spherical Coordinates: Derivatives

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Differential Equations: Implicit Solutions

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

Untitled

Differential Equations: Solutions and Derivatives

Explores differential equations solutions, derivatives, differentiability, composite functions, and continuous functions.

Canonical Transformations: Existence and Equations

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

Differential Equations: Solutions and Monotonicity

Explores solutions of differential equations and their monotonicity properties.

Advanced Analysis II: Sequences and Integrals

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

Quantum Mechanics: Jacobi Identity and Gauge Invariance

Explores Jacobi identity, gauge invariance, and conservation laws in quantum mechanics and classical physics.