Lectures related to Algebraic equation

Nonlinear Equations: Convergence and Taylor Polynomials

Explores nonlinear equations, emphasizing convergence and Taylor polynomials for function approximation.

Explains the Bioche rule for solving trigonometric equations using substitutions and tests of invariance.

Intersection Numbers: Algebraic Counting Solutions

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

Complex Numbers: Operations and Applications

Explores complex number properties, roots, and polynomial equations in the complex plane.

Nonlinear Equations: Fixed Point Method

Covers the topic of nonlinear equations and the fixed point method.

Galois Theory: Solvability and Radical Extensions

Explores solvability by radicals in Galois theory and the Galois/Abel criterion for solvability.

Tests of Invariance in Polynomial Equations

Explores testing invariance in polynomial equations, emphasizing solution identification and variable changes.

Sequences: Definitions and Examples

Covers solving equations over complex numbers, sequences, induction, and properties of complex numbers.

Complex Polynomials and Factorization

Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.

Solving Z² = W with Cartesian Method

Explores solving Z² = W in the complex plane using the Cartesian method.

Block Pulled by a Spring: Dynamics

Covers the dynamics of a block connected to a spring, deriving equations of motion and solving for key time points.

Linear Equations: Introduction and Solutions

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

Polynomial Roots: Finding Solutions and Division

Explains how to find solutions for polynomial equations and perform polynomial division.

Bioche Rules: Equations and Invariance

Explores invariance in algebraic equations and demonstrates solving trigonometric functions.

Absolute Values: Equations and Inequalities

Explores absolute values in equations and inequalities, focusing on solving |f(x)| = g(x).

Quadratic Equation: Programming Solutions

Covers the programming of a script to calculate the solutions of quadratic equations.

Gaussian Lemma III: Irreducibility and Primitive Polynomials

Explains irreducibility in polynomial equations and the properties of primitive polynomials.

Equilibrium in 3D: System Isolation and Constraints

Covers the equilibrium conditions in 3D, system isolation, free-body diagrams, and constraints.

Complex Numbers: Equations and Constructibility

Explores polynomial equations in complex numbers, constructibility conditions, roots of unity, and Fermat primes.

Partial Differential Equations: Equations and Solutions

Explores partial differential equations, focusing on chapter 6 equations and their solutions through Fourier series and variable separation methods.