Differential Operators: Notation and Terminology

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Differential Operators: Gradient and Divergence

Introduces differential operators, gradient, and divergence in vector fields.

Differential Functions: Definitions and Notations

Covers the definition of differentiable functions and introduces the concept of differential functions.

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Differential Operators: Theorems and Proofs

Covers the concept of differential operators and presents theorems and proofs related to scalar and vector fields.

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Differentiation and Coordinate Changes in Multivariable Functions

Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.

Connections: motivation and definition

Explores the definition of connections for smooth vector fields on manifolds.

Vector Analysis: Fundamentals and Applications

Covers fundamental concepts of vector analysis and their applications in science and engineering.

Vector Analysis: Applications and Operators

Explores vector fields, potentials, Fourier analysis, and differential operators in scalar fields.

Functions of LR: Differentiability

Explains differentiability in LR functions and introduces the Jacobian matrix.