Lectures related to Development Limit: Order 1 and 2

Taylor Polynomials: Correction Term

Explores the correction term in Taylor polynomials, showcasing its role in refining function approximations.

Error Analysis and Interpolation

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Linear Algebra: Abstract Concepts

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Approximation of Functions by Taylor Polynomials

Explores the theory and application of Taylor polynomials for function approximation and limit calculations.

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Taylor Polynomials: Definition and Approximation

Covers Taylor polynomials for function approximation and their properties, with examples.

Gauss-Legendre Quadrature Formulas

Explores Gauss-Legendre quadrature formulas using Legendre polynomials for accurate function approximation.

Taylor Polynomials and Approximations

Explores Taylor polynomials and approximations for various functions, emphasizing derivative equality and polynomial development around a specific point.

Polynomials on a Field: Basics and Operations

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Taylor Polynomials: Approximation and Generalization

Introduces Taylor polynomials for function approximation, starting with linear and quadratic forms and then generalizing to higher orders.

Complex Roots and Polynomials

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.