Lectures related to Application to Recurrence Defined Sequences

Nonlinear Equations: Fixed Point Method Convergence

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Fixed Point Theorem

Explores fixed point theorems, recurrent sequences, and convergence properties, emphasizing the significance of fixed points in analysis.

Continuity and Fixed Points: Understanding Functions

Explores continuity, fixed points, and bijective functions in graphs.

Continuous Functions: Integrability and Examples

Explores continuous functions and integrability through practical examples.

Newton Method: Data Interpolation

Covers the Newton method for finding zeros of functions using data interpolation.

Orbit of a G-ensemble

Explores orbits in a G-ensemble, functions of fixed points, and G-equivariance.

Real Functions: Definitions and Properties

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

Functions and Periodicity

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

Limits and Continuity

Covers limits, continuity, and the intermediate value theorem in functions.

Functions: Limits, Continuity, Differentiability

Explores the origin of functions, continuity, differentiability, and the physical representation of chemical bonds.

Limit of Functions: Convergence and Boundedness

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

Continuity of Functions: Definitions and Notations

Explores the continuity of functions in R² and R³, emphasizing accumulation points 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.

Limit of the Quotient and Periodicity

Explores the limit of the quotient for sequences and the periodicity of functions.

Points Fixes in G-sets

Explores fixed points in G-sets, applications between sets, and the construction of orbits.

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Implicit Functions Theorem

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Differentiating under the integral sign

Explores differentiating under the integral sign and continuity of functions in integrals.

Functions: Differentials, Taylor Expansions, Integrals

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Analysis I Exam Solutions

Provides solutions to an Analysis I exam, covering various topics.