Lectures related to Finite Element Modeling: Systematization and Integration

Generalized Integrals and Convergence Criteria

Covers generalized integrals, convergence criteria, series convergence, and harmonic series in analysis.

Explains the integration of Taylor series for CnR class functions.

Covers the integration of limit expansions and continuous functions by pieces.

Explores elementary cases of generalized integrals, convergence criteria, and the interpretation of integrals of type i and ii.

Improper Integrals: Convergence and Comparison

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

Development of Taylor Polynomials

Covers the development of Taylor polynomials of order p around a point x.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Numerics: semester project

Covers the semester project on numerics, focusing on adaptive algorithms and multistep methods.

Limit of Functions: Convergence and Boundedness

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

Geometric Series: Convergence and Limit

Explores the convergence and limit of geometric series, demonstrating mathematical properties and applications.

Riemann Integral: Convergence and Limit Process

Explores Riemann integral, convergence, and limit processes, emphasizing continuity and monotonic convergence.

Limit of a Sequence

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

Matrix Operations: Trends and Convergence

Explores matrix operations, trends, and convergence conditions with a focus on clear definitions and examples.

Improper integrals: Techniques and Examples

Covers improper integrals techniques and examples, exploring convergence and absolute convergence.

Analysis I Exam Solutions

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

Banach Spaces: Reflexivity and Convergence

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Integration of Functions: Series and Limits

Covers the integration of functions through series and limits, focusing on the development of limit expansions and the integration of entire series.

Iterative Methods for Linear Equations

Covers iterative methods for solving linear equations and analyzing convergence, including error control and positive definite matrices.

Convergence and Closed Sets

Explores convergence of sequences in closed sets and the importance of understanding convergence in relation to closedness.

Fourier Series: Understanding Periodicity and Coefficients

Explores t-periodic functions in Fourier series, discussing intervals, propositions, and variable changes for coefficient calculation and series convergence.