Lectures related to Vector Analysis: Fundamentals and Applications

Introduces vector definitions, displacement, addition, and applications in geometry.

Covers orthogonal vectors, unit vectors, and the Pythagorean theorem in R^m.

Covers differential operators, vector analysis, Fourier analysis, and potential fields with applications to gravity.

Linear Lie Groups: Definitions and Theorems

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

Euclidean Spaces: Properties and Concepts

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

Analytical Geometry: Vectors

Introduces the basics of analytical geometry, emphasizing vector representation, operations, and applications in geometry.

Continuum Mechanics: Theory and Applications

Covers the basics of continuum mechanics, including constitutive laws, stress, dynamics, and fluid motion.

Scalar Products in 2D and 3D Geometry

Explores the scalar product, vector lengths, angles, norms, and rotations in 2D and 3D spaces.

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: Gradient and Divergence

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

Differential Operators: Theorems and Proofs

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

Vector Spaces in R2 and R3

Covers vector spaces in R2 and R3, including planes and lines.

Tensor Transformations

Introduces tensor transformations, rotation matrices, and differential operators in mechanics.

Analytical Geometry: Vectors and Operations

Covers the fundamentals of analytical geometry, focusing on vectors and their operations.

Vectors and Kinematics

Introduces vectors in a solid reference frame and explains the importance of determinants in interpreting vector products and coordinate changes.

Objective function, Preconditioning

Explores the condition number in optimization and the technique of preconditioning.

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Linear Algebra: Matrices and Linear Applications

Covers matrices, linear applications, vector spaces, and bijective functions.

Differential Operators: Notation and Terminology

Covers the basics of differential operators and derivatives for n-tuples and vector fields.