Development Limit: Order 1 and 2

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Related lectures (28)

Page 2 of 3

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

Polynomials: Definitions and Operations

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.

Taylor Polynomials Exercise

Covers the calculation of Taylor polynomials and error bounds for function approximation.

Taylor Series: Basics

Covers Taylor series, polynomial approximations for function behavior, coefficient finding, and error estimation.

Stein Algorithm: Polynomial Identity Testing

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Reed Solomon Codes: Basics and Applications

Introduces Reed Solomon Codes, their applications, polynomial definitions, interpolation, roots, and the Fundamental Theorem of Algebra.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Taylor Polynomials: Approximating Functions with Taylor Polynomials

Delves into Taylor polynomials, showcasing how higher orders improve function approximations and how they can be used to calculate limits.