Partial Differential Equations: Basics and Classification

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Canonical Transforms: Hamilton-Jacobi Equation

Explores canonical transforms and the Hamilton-Jacobi equation, emphasizing explicit solutions and initial 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.

Derivatives and Tangent Planes

Covers derivatives, differentiability, and tangent planes for functions of one and two variables.

Distributions and Laplace Transform: Key Concepts

Discusses distributions, the Laplace transform, and their applications in mathematical analysis.

Functions with Values in R^m

Explores functions with values in R^m, gradients, derivatives, and the Jacobian matrix in multiple dimensions.

Differential Equations: Existence and Uniqueness Theorems

Covers the existence and uniqueness of solutions for differential equations.

Differential Equations: Solutions and Derivatives

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

Differentiability and Composition

Covers differentiability, composition of functions, partial derivatives, Jacobian matrix, and polar coordinates.