Lectures related to Quadratic formula

Completing the Square in Quadratic Polynomials

Demonstrates completing the square in quadratic polynomials for factorization simplification.

Complex Roots: Conjugate Pairs and Quadratic Equations

Explores complex roots, conjugate pairs, and quadratic equations solving strategies.

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

Covers the basics of ray tracing, including ray generation, intersection with geometric shapes, and distance calculations to planes, setting the foundation for implementing a ray tracer.

Complex Numbers and 2x2 Matrices

Covers complex numbers, quadratic equations, solutions in C, and 2x2 matrices.

Mild Dissipative Surface Dynamics

Explores mild dissipative surface dynamics, including conservative behavior and ergodic functions.

Simpson's Rule

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

Complex Eigenvalues Appendix

Covers the factorization of polynomials with complex coefficients and diagonalizability of matrices.

Quadratic Equation: Programming Solutions

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

Complex Numbers: Argument and Polar Method

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

Decomposition: Simple and Quadratic Factors

Explores the decomposition of a function into simple and quadratic factors.

Linearly Independent Solutions and Quadratic Equations

Explores linearly independent solutions in quadratic equations and the role of constants in trigonometric solutions.

Optimality Conditions: Quadratic Functions

Covers the formulation of quadratic functions and optimality conditions for finding the global optimum.

General Solutions of Differential Equations

Explores general solutions of differential equations with a focus on x

Examples: Polynomial Factorization

Covers polynomial factorization examples and polynomial division in complex numbers.

Mathematical Exercises: Functions and Equations

Covers mathematical exercises on functions, equations, and trigonometric functions.

Conic Synthesis in the Plane

Explores the synthesis of conic sections in the plane, covering eccentricity ratios and parametric equations.

Square Roots and Complex Numbers

Explores square roots in quadratic equations, complex numbers, Fermat prime numbers, and the Gauss-Wantzel theorem.

Equations and Inequalities on the Reals

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

Strong Convexity and Convergence Rates

Explores strong convexity's role in faster convergence rates for optimization algorithms.