Lectures related to Rational Powers: Definition and Properties

Limit in a Point: Definition and Examples

Covers the concept of limit in a point with definitions and examples.

Analyse II: Directional Derivative

Covers the concept and calculation of directional derivatives in multivariable calculus.

Convergence of Sequences

Covers the convergence of sequences and how to calculate limits for convergent sequences.

Vector Calculus: 3D Orientation and Cross Product

Covers 3D orientation, cross product, and volume calculations using mixed product in vector calculus.

Vectors: Fundamentals

Covers the basic concepts related to vectors, including their definition, operations, and properties, as well as applications through examples and the Varignon's theorem.

Integrals of Paths

Covers the concept of integrals of paths with examples and applications.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Partial Derivatives and Functions

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

Jacobian Matrix: Derivative of Composite Functions

Explains the Jacobian matrix and derivative of composite functions with examples.

Integer Cones

Covers the concept of integer cones and Carathéodory's theorem with illustrative examples.

Convex Functions

Covers the properties and operations of convex functions.

Trigonometric Polynomials: Periodicity and Fourier Coefficients

Explores trigonometric polynomials, periodicity, and Fourier coefficients in mathematical analysis.

Linear Algebra Basics

Covers the basics of linear algebra, including rank, differentiable applications, and submersions.

Linear Algebra: Multilinear Forms

Introduces multilinear forms in linear algebra, emphasizing clarity and logic in presentation.

Limit of a Sequence

Explores the limit of a sequence and its convergence properties, including boundedness and monotonicity.

Advanced Analysis II: Recap and Open Sets

Covers a recap of Analysis I and delves into the concept of open sets in R^n, emphasizing their importance in mathematical analysis.

Matrix Calculus: Rank and Decomposition

Covers matrix rank, determinant, and decomposition in linear algebra.

Partial Derivatives: Higher Order and Applications

Covers the concept of partial derivatives of higher order and their applications in various contexts.

Linear Algebra: Compositions and Injections

Explores compositions and injections in linear algebra, emphasizing their importance.