Lectures related to Diophantine equation

Introduces linear equations, matrices, systems of equations, and solution sets for 2 or 3 unknowns.

Digital Controller Design: Pole Placement Technique

Covers digital controller design, focusing on discrete-time models and the pole placement technique.

Regulator Polynomial RST: Classic Servo Systems

Explores classic regulator systems, polynomial degrees of freedom, servo model modifications, and system adjustment through simplification and zero invoicing.

Newton's Method: Convergence and Criteria

Explores the Newton method for non-linear equations, discussing convergence criteria and stopping conditions.

Fermat's Equation: Integral Solutions and Gaussian Integers

Discusses Fermat's equation and Gaussian integers' properties.

Polynomial Regulator Design

Covers the design of polynomial regulators using the RST method.

Linear Equations and Matrices

Covers the fundamentals of linear equations, systems, solutions, and graphical representation.

Fermat Equation: Solutions and Coprime Numbers

Explores solutions of the Fermat equation and the importance of coprime numbers.

Equations and Inequalities on the Reals

Covers algebraic identities, linear equations, and rational inequations on the real numbers.

Matrix Determinant: Factorization and Linear Equations

Covers the determinant of a matrix, factorization, and linear equations with infinite solutions.

Linear Equations: Solutions and Matrices

Explores solving linear equations, matrix uniqueness, and reduction methods with examples.

Linear Equations: Introduction and Solutions

Covers the introduction and solutions of linear equations, including methods for solving systems and determining the number of solutions.

Non-linear Equations: Dichotomy Method

Explores non-linear equations using the dichotomy method for finding zeros with tolerance.

Finite Element Method: Quadratic Elements

Explores the precision of finite element models and higher order asymptotic estimates.

Linear Equations and Systems

Covers linear equations with multiple variables and systems, including solutions and consistency criteria.

Parametric Equations and Cartesian Coordinates

Explores parametric equations, Cartesian coordinates, lines equations, and geometric angles between lines.

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Linear Equations: Elementary Operations

Explores systems of linear equations, elementary operations, augmented matrices, and Gaussian elimination algorithm.

Gaussian Elimination Method

Covers the Gaussian elimination method for solving linear equations using row operations and equivalent matrices.

Systems of Linear Equations and Matrices

Covers the definition of linear equations, systems, solutions, and representations in 2D and 3D.