Lectures related to Continuity and Limits

Limits of Functions: Calculus Methods

Explores the concept of limits of functions of several variables and methods for calculation, including criteria based on convergent sequences and the 'two gendarmes' theorem.

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Coordinate Systems: Applications and Transformations

Explores coordinate systems, including polar and curvilinear coordinates, and their transformations.

Limits of Functions in Several Variables

Explores limits of functions in several real variables, including the two gendarmes theorem and the minimum and maximum theorem on compact sets.

Limits and Continuity

Covers the concept of limits and continuity in real analysis.

Relations in Computer Science

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Derivatives and Functions: Definitions and Interpretations

Covers the definition of derivative functions and their interpretation, focusing on differentiability, velocity, and curve lengths.

Derivability and Composition

Covers derivability conditions, function composition, Jacobian matrix, and chain derivation.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Limit of Functions: Convergence and Boundedness

Explores limits, convergence, and boundedness of functions and sequences.

Advanced Analysis II: Polar Coordinates

Covers the advanced analysis of functions in polar coordinates.

Gradient and Taylor Formula

Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.

Infinite Limits at a Point

Explores infinite limits at a point and their properties, including lateral infinite limits and comparisons with sequences.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Differentiability of Functions of Several Variables

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

Existence of y: Proofs and EDO Resolution

Covers the proof of the existence of y and the resolution of EDOs with practical examples.

Advanced Analysis II: Isoclines Method

Explores the Isoclines Method and solutions of differential equations with tangents.

Harmonic Forms: Main Theorem

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