Lectures related to Curvilinear Integrals: Fundamentals

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Explores interior points, boundaries, adherence, and compact sets, including definitions and examples.

Geometrical Aspects of Differential Operators

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

Multivariable Integral Calculus

Covers multivariable integral calculus, including rectangular cuboids, subdivisions, Douboux sums, Fubini's Theorem, and integration over bounded sets.

Green-Riemann Formula: Curvilinear Integrals

Covers the Green-Riemann formula, connectedness by arcs, parametrization of curves, and open simply connected domains in the Oxy plane.

Analysis 1: Sequences, Intervals, and Absolute Value

Covers sequences, intervals, and absolute value concepts in Analysis 1.

Symmetries and Groups in Quantum Mechanics

Covers the role of symmetries and groups in quantum mechanics, focusing on SU2 and SU3, their properties, and implications for physical theories.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Curvilinear Integrals and Conservative Fields

Explores curvilinear integrals, conservative fields, and their implications in various contexts.

Manifolds: Charts and Compatibility

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Vector Fields Analysis

Explores vector fields analysis, covering curvilinear integrals, potential fields, and field connectivity conditions.

Compact Embedding: Theorem and Sobolev Inequalities

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Curvilinear Integrals, Conservative Fields, and Green's Theorem

Covers curvilinear integrals, conservative fields, and Green's Theorem with examples.

Advanced Analysis II: Eigenvalues and Compact Sets

Covers the reconstruction of a table using diagonal matrices and explores extreme values and set definitions.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Convergence in R^n

Explores open and closed subsets, convergence in R^n, and bounded sequences.

Curve Integrals: Gauss/Green Theorem

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.

Analysis I: Decreasing and Growing Functions

Explores decreasing and growing functions, bounded sequences, and limit existence.

Continuous Functions on Compact Sets

Explores continuous functions on compact sets, discussing boundedness and extremum values.