Concept

Bézout's identity

Related lectures (27)

Polynomial Division & Observer/Controller Approach

Covers polynomial division and observer/controller approach with step-by-step examples.

Explains the Euclidean algorithm for polynomials over a field K, illustrating its application with examples.

Explores lag compensator design in control systems, emphasizing phase margin and steady-state error improvement through practical examples.

Ziegernichels Tuning

Covers Ziegernichels tuning, a method to quickly tune PID coefficients for stable and unstable systems.

Ideals: Polynomials and Definitions

Explores ideals in K[X], including PGCD, uniqueness, coprimality, and theorems of Bézout and Gauss.

Projective Plane Curves

Introduces projective plane curves, degrees, components, multiplicities, intersection numbers, tangents, and multiple points, culminating in the statement of Bézout's theorem and its consequences.

Euclid and Bézout: Algorithms and Theorems

Explores the Euclidean algorithm, Bézout's identity, extended Euclid algorithm, and commutative groups in mathematics.

Polynomial Methods: GCD Calculation Summary

Covers the calculation of the greatest common divisor using polynomial methods and the Euclidean algorithm.

Polynomial Factorization and Decomposition

Covers polynomial factorization, irreducible polynomials, ideal decomposition, and the theorem of Bézout.

Loop Shaping: Goals

Focuses on designing a controller to meet specific requirements by shaping the response of closed-loop transfer functions.

Number Theory: GCD and LCM

Covers GCD, LCM, and the Euclidean algorithm for efficient computation of GCD.

Polynomial Rings and Irreducibility Criteria

Covers polynomial rings, irreducibility criteria, and algebraic structures in fields.

Lead Compensator Design

Focuses on designing lead compensators for PD controllers to improve phase margin and reduce steady-state error.

Integers: Sets, Maps, and Principles

Introduces sets, maps, divisors, prime numbers, and arithmetic principles related to integers.

Introduction to Algorithms

Introduces algorithms as problem-solving procedures, covering complexity, correctness, and implementation in various languages.

Algebra: Integer Numbers and Principles

Introduces integer numbers, well-ordering, induction principles, GCD, LCM, and Bezout's theorem.

Algorithm Basics: Ingredients

Covers algorithms, data, loops, control structures, and the Euclidean algorithm.

Polynomials: Theory and Operations

Covers the theory and operations related to polynomials, including ideals, minimal polynomials, irreducibility, and factorization.

Function Composition and Integers

Covers function composition and integers, including properties and examples.

Polynomials: Roots and Factorization

Explores polynomial roots, factorization, and the Euclidean algorithm in depth.