Lectures related to Cubic equation

Powers and Roots: Understanding Irrational Equations

Delves into powers and roots, emphasizing irrational equations and the disjunction of cases.

Geometric Constructions: Duplication of the Cube

Explores the historical significance and geometric methods for duplicating the cube.

Newton's Method: Convergence and Conditions

Explores Newton's method convergence conditions and fixed-point interpretation.

Geometry: Euclidean Elements & Vitruvius

Explores Euclid's first proposition, ancient symmetria, and Vitruvius' architectural figures.

Complex Numbers: Argument and Polar Method

Introduces the argument of complex numbers and the polar method, demonstrating their application in finding roots.

Fixed-Point Methods and Newton-Raphson

Covers fixed-point methods and Newton-Raphson, emphasizing their convergence and error control.

Algebra: Quadratic Trinomial

Explores quadratic trinomials, absolute values, Vieta's formulas, and graphical representation of equations.

Roots of Real Numbers

Explores the properties and applications of roots of real numbers through practical examples.

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Complex Polynomials and Factorization

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

Solutions of Homogeneous Linear Differential Equations

Covers the solutions of homogeneous linear differential equations and how to find linearly independent solutions.

Simpson's Rule

Covers Simpson's rule for numerical integration and its accuracy for polynomial functions.

Roots of n-th Degree

Covers the concept of roots of n-th degree in complex numbers and their exact solutions.

Polynomial Root Finding

Explores polynomial root finding methods based on evaluating potential roots from divisors of the constant term.

General case of degree two polynomials

Explores Viète's formula for finding roots of degree two polynomials and their significance.

Spatial Response and Convolution

Covers the spatial response of systems, including the calculation of the center of mass and convolution.

Polynomials: Irreducibility and Vieta's Relations

Explores polynomial irreducibility and Vieta's relations in depth.

Lagrangian Mechanics

Covers Lagrangian mechanics, a method simplifying equations of motion by focusing on energy concepts and generalized forces in complex systems.

Ellipses and Conics

Explores ellipses, conic sections, Kepler's laws, and geometric reconstruction in architectural modeling.

Geometric Operations: Inversion & Orthogonal Circles

Explores geometric operations like inversion, orthogonal circles, and cube duplication, emphasizing historical significance and modern construction methods.